Im new on here so apologies if this isnt needed or relevant any more!
I moved from the north of england to London a couple of times. My rule of thumb for cost of living is as follows:
Get a good map!
Use the M25 (the big motorway that encircles London and creates a natural line around the inner and outer parts) as a guide for pricing - living inside the M25 means usually that prices for renting flats etc are higher than if you live just outside. I live in West London, lovely area called Ruislip which has two main tube lines into central london on my doorstep, which take about 30 minutes each.
Get a good tube map so you can live near good rail/tube links. Sort out the cost of travel as this can be quite expensive - Transport for London has a great web site but i am not allowed to give that to you on here.
Get cheap daily travel sorted out - I bought an Oyster card which just about halves the cost of tube fares into the capital and/or other areas. I still run a car, have a nice modern flat which i share at a cost of £550 a month plus utility bills (the new builds are often done as two bed two bath so singles can share). I used Foxtons Estage Agency as they were the nicest people and had some lovely flats to show us.
I love West London, its so nice to just get off into the countryside on the bus or train or take the car into the Home Counties on weekends. Not far from Heathrow (15 miles) and Luton (25 miles) for cheap holiday destinations/returning home.
My salary is around the same as yours, so i guess if you take my advice you will go as far out of the city as you can. The further you do go the more you save.
We find that a 45 minute to 1 hour commute is acceptable. Where we live the tubes tend to travel more overground so its not too hot or claustrophobic.
We shop at local discount stores and do a lot of free stuff - walking, parks, museums etc. Its a great place to be!
Hope the move goes well.