Perhaps but not necessarily. I find the NHS private practice offices often charge more.
The price I would expect my patients to pay in Central London is between £700 and £1500 depending on what is required. You may need to be injected with a drug called gadolinium and the price is calculated by the number of 'parts' or the complexity. One part is £700. So nobody can give you a price without seeing the referral letter or request form unless they are just charging on the safe side.
Outside London everyone expects prices to be lower, but this is not necessarily true with MRI as most of the costs are identical
PM me if you would like a firm price based on the above
Best wishes