I have done a thorough research on this and got the following results. Now I am sorry I booked my Ryanair ticket and am considering going to the UK by ferry as that way I can take my own car. Please see below as it may be useful to you:
AVIS and Budget accept Irish Visa Debit but demand you have your drivers licence for 3 years. Security deposit depends on the type of vehicle but for a normal sized vehicle its not more than 70 or 90 GBP - values differ when you speak to the branch and/or customer service team.
HERTZ branch in Stansted says they accept Irish Visa Debit, customer service team says they don't. 1 year full drivers license is all they require. Deposit is 300GBP according to Customer Service team, but 200 GBP says branch.
Thrifty are really strange - I rang them twice to make sure they would accept my Irish VISA debit card, I was told all was fine, they would accept it, but for me I have to see it to believe it so I emailed them and asked them, and they replied that they do NOT accept my Irish Visa card because it is not UK based - this contradicts what I was told over the phone. Deposit is GBP 150 and they accept full drivers license as long as I have it for at least 1 year.
Enterprise accepts Irish Visa Debit card in the UK. Deposit is GBP 200. 1 year drivers license. but I do not have this in writing which means by the time I get there conditions may differ!
Greenmotion says in the branch they accept irish visa debt but I have not got that in writing. deposit is GBP 1500 but if you purchase insurance of 18 GBP a day they reduce deposit to GBP 150. This is all over the phone, I do not have it in writing and I find it hard to trust after my experience with Thrifty above outlined where over the phone the same branch says one thing that then they (the same branch) contradicts by email.
Alamo/Europcar accepts Irish debit card, deposit is GBP 250, 1 year drivers license. Again I haven't got that in writing.
After this experience, I am really put off renting a car in the UK... as I am not sure that when I get there they may say very sorry but we cant give you a car because your VISA debit card is not UK based or something else... or they may ask me for a deposit of GBP 1000 frozen on my account which means I will be able to enjoy my holiday as I will not have enough money.
All things considered, I think that if you have a Debit card, the best is to go by ferry and take your own car, it takes longer and is more tiring but you have more freedom. I also checked with my insurance company and they cover me abroad, so I am not yet sure how I am going and even if I will bother going to the UK at all.