My thoughts on the itinerary:
Ireland/Scotland/London only - 21 days
Paris and surrounding places (add Normandy and Mount St Michel) - 10 days
Italy (add Milan, Cinque Terra, Florence and further south of Rome if you have time) - 21 days
Total of 52 days .. this leaves 4-6 days to add a day or two to the above or to use as travel days.
Budget has been mentioned several times already so I won't comment (to much) on it ... I am planning a 5-6 week trip (2 weeks London/Cotswolds and 3+ weeks Netherlands/Belgium/Luxembourg) and my budget is 8k (not counting airfare) ... I take it you are solo since you always use "I" and not "we" so just a reminder a single room will cost almost as much as a 2 person room (don't assume a room for 1 is half the cost of a room for 2) ... didn't see how you were getting from place to place but that will be a huge cost whether you take trains or rent a car.
My first recommendation would be to create a spreadsheet ... I know there are others on this forum who love spreadsheets also and am sure they will agree it is an invaluable tool to organize your trip ... create separate workbooks for each place (1 workbook for ISE, 1 for Paris, 1 for Italy so it doesn't get too long and overwhelming ... list everywhere you want to go, how you will get from place to place, where you will stay, daily allowance for food, sites you want to visit (are there entry fees?), etc... and how much it will cost ... you will be surprised on how quickly this all adds up ... it will take time to build and you'll be constantly fine-tuning but you'll see the big picture in black and white when it's done.
A few more recommendations in no particular order ... some have already been mentioned and I totally agree with them:
1) Always reserve refundable rooms (look for places that don't require pay now to reserve, instead look for pay at the hotel) ... and keep track (on your spreadsheet of course) of what is reserved so if you need to cancel you won't miss any and be out the money ... go back every so often and search again, sometimes the price actually goes down or you find a place you like better for less ... if so, book it first and then cancel the older reservation (and update the spreadsheet)
2) Trip insurance ... I got a 1 year basic policy from Allianz for myself and wife and it cost about $125 (this was about 5 years ago so not sure of costs now) ... be sure it includes coverage if you need to be evacuated back home
3) Use a credit card with no foreign transaction fees ... and one that provides extra coverage for a rental car if you go that route
4) Plan for down days (every 7-10 days) to do laundry, sit at a cafe and watch the world go by, get up late/go to bed early to recharge the batteries, etc...
5) Build in flexibility ... in 8 weeks, you will get rained on more than once ... don't plan a big outdoor day the day before you are moving on ... be ready to swap an indoor day (museum) for an outdoor day (foot tour of Paris/London/Rome) if the weather doesn't cooperate
I have more but need to get back to work :-)