Why didn't you take this - that you need more money - into account before accepting the offer?

@ThorbjørnRavnAndersen I haven't accepted an offer yet

@Donald I don't have a home at the moment so I can't downsize. The travel expenses account for the 3 days working from the office that they require, working from home the other 2.

@JoeStrazzere thanks. This is actually what I just found out the recruiter is going to talk about with the company, to see if a slightly higher salary can be negotiated with a justification of why.

looks like you're putting yourself in a difficult situation. If you loose that job and have to accept a lower salary, how are you going to pay that mortage?

@Lyall - You made it sound like you had already accepted a specific compensation. My advice would have been different if I knew you were still negotiating. You certainly could downsize the homes you are looking at.

In the US, employers can offer transit passes to employees as a benefit that is tax-free to the employee. You might check to see whether your employer offers this benefit.

The commute sounds utterly preposterous. Does the 45 minutes by train mean door-to-door, or just the part whilst your inside the carriage (i.e. not including walking time to/from the station at each end, waiting time, etc.)? And 1.5 to 2.5 hours each way by car, on top of the working day, is utterly unsustainable. I would write the job off as being patently too far away to consider.

Some companies do commuter reimbursement, you can inquire. It would be(/have been) a reasonable salary negotiation tactic to compare (unnamed) other companies' total packages incl. that. b) Never call commute 'travel costs'. 'Commute' is involuntary and costs related to your home-office distance; '(personal) travel' is voluntary and discretionary, like seeing the Pyramids.

You could try asking for a once-off signing bonus, instead of another increase in salary, and explain your increased commuter cost. But it's better not to keep coming back for more, unless you undersold yourself the first time. Anyway as the others said these are your costs not the employer's, unless you can make the case that you could WFH for another employer.

"The pay increase would be approx. £1,300/month but I'm intending to put most (if not all) of that towards a mortgage for my first home" — I presume living closer to work in the meantime isn't an option?

Many companies in the US do not have parking for employees who have to drive to work. Therefore, the employees have to pay for parking. I had an employer who advertised "employee parking", only to discover, once hired, that they had a small lot and a long waiting list to get into it. At my orientation, they handed me a list of local parking lots with prices from $40 to $100+/month. I chose to walk farther and pay less. Also, the estimated wait to get into the company lot went from about 20 months when I started to nearly 3 years when I left (nobody was leaving the company).

You should absolutely 100% not take the hit of commuting longer distances and paying out of pocket. This could effectively be a pay cut if you judge by how many hours you spend for work (including commuting). I would strongly advise you to negotiate working from home.

Where I live, commute by transit takes 2x-3x as long as by car instead of the other way around.

@Steve the OP is likely to have other things to take into account, but central London commutes are over an hour for a lot of people (which this probably isn't because car is an option). Mine is a bit over an hour but the train is relaxing enough or I can work, and that's half the time. Driving takes a similar time, similar cost with fuel and sometimes parking, and is far worse, but I very rarely have to do it.

@shoover that's highly variable, even within a small area. Efficient public transport within a city is often radial. If you live in one suburb and work in another, the route can be circuitous and/or slow.

If they don't offer reimbursement, see if your locality offers something like the US's TransitChek, which lets you use pre-tax money from your salary to pay for transit.