I have a 2 hour commute each way to London and work full time. Try it and see how you get on.
It is not cheap my annual season ticket is a lot, but it is cheaper than moving to or nearer London. I like where I live and my children are settled into nursery and school, so commuting works for us as a family at the moment
There a (few) people, who do commute long distance . The key to a long commute is to be organised and have a good support network around you. Do you have this?
Factor in the cost of your season ticket off your salary each year because that is how much you will really be earning
Also factor in a contingency plan for things going wrong. The trains can and do get messed up often. Be prepared for that.
If you have children think about who can step in for you if there was an emergency of some kind. E.G. child has accident, school closed during the day suddenly. These are worse case scenarios, but remember even if you down tools straight away at work and rushed for the train. Initially you are still over 100 miles and two and a bit hours away from home, so someone had to step in, whilst you are a travelling
If you have children are you they/ prepared to see them quite as much?
There maybe times when you are not home for bed time because train has messed up and you will be leaving early again next morning. It is not easy, but my children are used to me travelling frequently and being away overnight with work.