Look at Hostelworld.com for places to stay and prices. You might want to book your first couple of days and last couple of days in advance. Easyhotel.com is a cheap hotel in London. NO frills, everything costs extra but if you can do hostels then this should work.
Have you thought of open-jaw tickets? Would save back tracking. Where you are flying home from is where you should visit last. If that be London, then do London last, not first. That way, you are where you are leaving from early and not trying to get there.
The arriving day is screwed up anyway. Jet lagged and tired. Have a train ticket or bus ticket or cheap airline ticket and go north to Scotland first. You can fly to Edinburgh or Glasgow or Aberdeen. Bus or train will take you most anywhere. Then work your way back, assuming you are flying home from London.
Car rental, if you can drive a stick, is fairly cheap. Gas, however is probably over 8.00 per gallon by now or even more. In Scotland, it might be worth renting for a couple of days to go and see the highlands. Bus and trains are sparse there.
I remember that when we were in Edinburgh, it was cheaper for the two of us to take the bus to Glasgow than it was to pay the gas for the car. Look at your itinerary and see where a car might be used. If it looks like it can, then rent one, if not, then bus or train.
I think you would like Inverness also. If you go, look at Johnny Fox pub for average food but great bands at night. A good place to stay would be
Ardgarry B&B -http://www.ardgarryguesthouse.co.uk/accommodation_tariffs.html
would be around 44-50 pounds for 2- per night, with great breakfast.
There are decent Hostels there with rates from 20L per person. Be sure to check the rating of hostels before you book. Would also book private if possible at hostels. My son did not and left a hostel with 5 days left on the bill and found another place to stay. It had a bad rating, but he did not do his research before he went.