This question is perhaps slightly too broad to give a definitive yes/no answer, as it highly depend on your personal circumstances and preference which I acknowledge that it is impossible to enumerate in a question.
I will instead provide where you can obtain more information as part of your research.
The estimates from Greater London Authority gives a median household income of £39,100, and a mean income of £51,770 in 2013/14. They did not specify, though in UK income is usually quoted before tax.
This is the latest data available for London, though if you do a back-of-envelope calculation using the annual mean wage growth of 2-4% pa, your income will still be well above the median/mean.
Two things to note:
- UK salary is almost always quoted before tax. You can use the take home salary calculator to calculate what your net income will be around. Take into account how much you are contributing to your pension and other benefits, as that will affect how much tax/ National Insurance you will pay.
- You are likely required to pay the tax bit for the private medical insurance (PMI). Assuming your PMI covers your wife and child, and taking your gross salary into account, the tax on PMI is likely to amount to a few hundred pounds.
Renting a decent 2-bedroom apartment in suburbs
The rent for a 2-bedroom apartment widely fluctuates in the 'suburb', which can refer to any of the outer London boroughs (covering a size of 1300+ sq. km, at least seven travelcard zones (from zone 3)) or tens of commuter towns outside Greater London.
You can have a look on property listing websites (e.g. Zoopla or Rightmove) to get an idea how much (or affordable, if any) they cost to rent.
A side note: if you decide to live somewhere outside walking distance from your office, you will need to take into account of the transport cost. There are quite a number of options, though they are generally not cheap (see e.g. travelcard (season ticket) cost).
Rent a car when needed (eg via car-sharing)
There are a number of car clubs operating in London, where you pay an annual fee to join and a hourly fee for using the car. Some of them allow you to do one-way journeys within London.
The Transport for London link above links to a number of car club, which you can get an estimate on cost depending on your usage.
Send the child to a kindergarten
This article gives a ballpark figure on how much different childcare options will cost.
Spend vacations in continental EU 1-2 times a year
This depends on your travel arrangements - the answer will be different if you are staying with a friend/relative as opposed to staying in a hotel. In general the cost you should consider consist of:
- The cost to travel to/from the destination (either by train or plane, see below)
- The daily running cost (which Lonely Planet provides a pretty good estimate)
One thing to note is that flight tickets tends to get very expensive during holidays (Christmas, Easter, during Summer and half-terms) - you might be more flexible at this stage, though when your child started school your options will be more limited.
Go to a restaurant 1-2 times a week
A dinner for two ranges from £30-£100+ depending on what you eat. Though going out with a 3-year-old probably eliminates the top-end restaurants as options and hence capping your cost.