I can't comment on the microlight permit part, as I know nothing about that.
On the rest of it...
I'm assuming you are leaving from the Republic and going to the UK only, and then returning to the Republic.
What you need is
1. A flight plan
2. A GAR form.
The flight plan, needs to be filed for your flight out of Ireland, and your flight back into Ireland. Internal UK flights don't need a flight plan.
I'm assuming you've used a flight plan before, but if you haven't the CAA in the UK does a good guide on them. See here
Don't be surprised when you can't close a flight plan on landing in the UK. They don't have a concept of closing flight plans in the UK, and it isn't an issue. You can try asking ATC (not a radio service (see later)) to send an "arrival message" for you, but there isn't much need. However coming back to Ireland, don't forget to close your flight plan on landing!
The GAR needs to be submitted to both UK customs and UK Special Branch (police force). You can find the latest copy by going to http://www.hmrc.gov.uk/
and entering "General Aviation Report" into the search box.
You need to fill this out, and fax to both UK customs & Special branch. (There is no need to send it to immigration for flights between UK & Ireland, as these are within the common travel area. If doing a UK to contential Europe flight, you need to send it to immigration instead of special branch).
Special branch requires 12 hours notice legally (though some polices request 24 hours notice). The fax numbers are shown on the GAR form, but sometimes these are old numbers, and you have the phone them on the phone number (also shown on the form) to get the current fax number. Some special branch forces want you to phone them for a confirmation number (to prove that they have received your fax) but this isn't a legal requirement. North Wales is one example of this.
Notice on the GAR form is required for Special Branch for both your Ireland to UK and UK to Ireland flights.
UK Customs require different notice periods, depending on where you are coming from/going to, and again this is shown on the GAR form. In your case, you need to give them four hours notice (by filing the GAR) of your Ireland to UK flight, and no notice is required of your UK to Ireland flight.
There is one exception to the requirement to file a GAR report to customs/Special Branch. If your airport first airport of arrival in the UK, and last airport leaving the UK is a designated airport, then no notice is required. A list of these airports are shown on the GAR form too. They tend to be the larger airports, which have airline traffic. Be careful, some of these are designated for only customs or only special branch, in which case, the other one still requires notification. If you arrive in the UK via one of these airports, then you don't need to notify your arrival, and if you leave from one of them, then you don't need to notify your departure.
The Irish situation is a little less clear. As it stands, Irish immigration don't care about your Ireland to UK flight, nor your UK to Ireland flight, PROVIDED everyone on board the aircraft is a UK or Irish citizen. If not then you must land at a port of entry.
Customs seem happy enough for you to land at any airport, once you let the airport operater know that you arrived from abroad. This was being reviewed during 2007, and customs promised to keep me informed of any changes, but I haven't heard any more yet, so assume it's still the same.
I hope that helps with the paper work, if you have any questions on it, feel free to ask.
On the practical side, I would say a few things to you.
1. Before your first trip, have a read of the UK CAA issued VFR guide. It guide you a total overview of vfr flight in the uk, and services that are available to you. Unfortunately, I can't find it on the CAA website at the moment...perhaps someone else can find it. If you can't find it, pm me your email address, and I'll email you an old copy....being old won't matter too much...it will give you the basics. But don't be put off...it's not that much different to Ireland.
2. Learn how to do a "Standard overhead join". They aren't used too much in Ireland, but in the UK they are very common.
Here is the CAA's guide to a standard overhead join.
3. The UK RT is slightly more formal.
The gospel here is called CAP413. You can find it here
The most important points to pick up from it are:
A) The correct response to ATC's request to "Pass your message"....you'll find it in CAP413, and you'll use it on almost every single time you contact ATC in the UK.
B) The difference between being told to "contact xxxx (atc unit) on 1xx.xx" and being told to "Freecall xxxx (atc unit) on 1xx.xx".
Contact means that your details have already been passed to the next ATC unit, and you only need to report your call sign to them. Freecall means that your details have not been passed to the next unit, and you'll need to use the full "Pass Your message" call when you call them up.
C) The different forms of air traffic service outside controlled airspace.
In Ireland, we only have a flight information service outside controlled airspace. In the UK there are three different services:
Flight Information Service
Basically, ATC will tell you about any important items that comes to their attention affecting your flight. They may not have any radar, and make no promise about telling you about any traffic...they may not know about traffic. Often units with radar will pass you traffic info on a FIS, but they still make no promise to tell you about everything.
Radar Information Service
Available from radar equipped units, and LARS units (see the VFR guide to see what a LARS is!)
With a RIS, ATC are radar equipped, and promise to tell you about any relevant traffic that they know about. Often ATC will not be able to give you a RIS because of their work load, and will instead offer a FIS.
Radar Advisory Service
Only available to IFR flights.
That's the bare basics of the differences. More can be found in the VFR guide, and on the CAA website, but the above is probably enough for practical purposes.
E. It's also important to know the differences between "Radio", "Information" and air traffic control. These are explained in both the VFR guide, and in CAP413 linked above. But very briefly,
Radio=often unmanned at small uncontrolled aerodromes. If it is manned, the person on the radio may not be able to see outside at all! They can't issue you instructions at all, but can provide info such as QNH, runway in use, where to park, etc.
Information. These can provide you with information when you are in the air, but can't issue instructions. eg. they can tell you there is someone on long final, but they can't tell you to go around...that's your decision. They do however issue instructions when you are on the ground. Basically when your on the ground, treat them like air traffic control...You need clearances for ground movement.
ATC...you always need clearances from when within their airspace.
4. UK airspace can be packed together much tighter than in Ireland. If you are going into fairly dense areas, such as around London, it would be very useful to have a GPS that you are familiar with using, and which has your route loaded. You are also much more likely to see traffic enroute in the UK, than in Ireland...almost guaranteed to spot at least one aircraft on any flight of any length in the UK, and probably much more.
5. Finially, there some some airspaces that you might not be familar with such as MATZ's and ATZ's. They aren't very difficult, and you can read all about them in the VFR guide (you getting the idea that that guide is valuable yet??
If you want to tell me your planned route when you have it, I can offer further advice specific to your flight.
Don't forget the obvious such as life raft AND life jackets. The Irish sea is very cold at any time of the year, but particularly this time of year! You won't last long in the water with life jackes alone, and you will be extremely hard to see (just your head sticking out of the water). The weather this time of year can be very changable too. Climb as high as you possibly can....better radar and rt coverage, and more time to deal with any potential problem.
Finially, I'd say that if you know all the above, you'll be like an old hand
I'm sure plenty of pilots fly to the UK without knowning the correct RT and services etc but you might as well learn the correct way, and at least sound like you know what you are doing
I hope that's of help, and I haven't made too many typos!.....I'm off to bed, and it's too late to proof read!