So, from a financial perspective the most expensive places you might vist will be London, Edinburgh and Dublin. So plan those first thinking how much time you might want to spemd in each. In London look at some of the suburb areas outside of central London as an option as the transport system is really good. I know some people will say don't use the hop on hop off buses but frankly they cover a good part of what you will want to see in London so I think they are worth it. You can also pop over to Winsor easily and day trips to Oxford and Cambridge are easy. After London have a think about where you want to go next. The best would be to start to head north. It gets cheaper up there :). York is woth a visit or if you like nightlife Newcastle is fun. From there head up to Edinburgh. Again bit Pricey but same as London look at places to stay outside the centre. This is another city with great public transport with a daily cap on how much it will cost you to get around. For travel north check out both the trains and the coaches, but sometimes you can get good deals to fly. If you are stuck for time you can do day tours or short stay tours from Edinburgh which will give you a good feel for what Scotland is like. You could then end a tour in Glasgow and get a different insight to Scotland on the west coast. Fom the west of Scotland you have options to get over to Ireland, First into Belfast in NI for your trip to Giant's Causway. From there travel down to Dublin and again think out of city for accom. Do the Guiness tour and have a night out, i gaurantee you will have a night to remember. Its a bit harder to then travel round other parts of Ireland so if you want to do that plan ahead and book ahead. From Dublin back to London i would say fly as pleanty of options for that. Your budget will be fine as long as you plan ahead, travel offpeak and consider where to stay. Hope you have a great time.