MPs all get the same salary, with only a small uplift for London MPs, but average incomes vary wildly across the country, so while £82k would be a lot in some parts of the country, it's not so significant in London. They have to pay for mortgages, food and bills out of that, just like everyone else. MPs have to spend most of the week in Parliament, which sits until late, so many of them have prodigious childcare bills as well - unless they have a non-earning partner who can look after them.
MPs from outside London can claim for the cost of travelling between their constituency and Westminster and can claim the costs of accommodation in London. Since the rules were changed in 2009, they can only claim for flat rental or hotel accommodation, so no more mortgage repayments. London MPs don't get travel or accommodation - they're regarded as commuters, just like their constituents.
Food on the estate is subsidised, but that's as much for the benefit of Parliamentary workers like clerks, cleaners and police officers as it is for the MPs. Late sittings mean that people don't have many other options for places to eat.
It certainly used to be the case that MPs routinely had outside interests, but being a constituency MP is pretty much a full time job now - much more so for those in marginal constituences than those with big majorities. A reasonable salary is essential if the role is to be accessible to the widest possible number of people.
I don't think the salary is that great for Londoners, but probably not so bad for those from elsewhere, especially where housing and childcare costs are much lower.
Also remember that only about 120 MPs at a time get to be ministers or committee chairs and qualify for the additional salaries. The vast majority will be stuck on the backbencher salary, regardless of how long they spend in Parliament or how much better they are at doing their job than other MPs.