These schemes work in different ways so I can’t say exactly how this particular one works.
However, when they say your pay rate is more, it certainly isn’t costing the agency any more to employ you. It is probably costing them less.
It may well be an umbrella scheme where you are officially employed by a third party you have no connection with other than it pays your wages.
Also bear in mind that the payroll or umbrella company needs to make money too, but hang on there is no more money. This is where a significant portion of your tax savings on travel will actually be to pay this company, reducing any benefit there may be (there may not be any benefit and you could be worse off).
The inflated rate may well be the rate per hour that is passed on to the umbrella company. However, will an additional percentage be sent for holiday pay? The answer is possibly not. Will an additional percentage be sent to cover employer’s NI? Possibly not. The umbrella company may also have a fee structure that means you pay a certain amount even in weeks where you may work very little. When these things are taken into account suddenly £1.50 more really doesn’t cover it.
The simplest thing you can actually do is to get paid straight PAYE. If you really wish to claim tax back, then you can do this yourself. Either go self-assessment or you can claim online without going self-assessment if your total cost of travel and subsistence is less than £2500 per year.
You just need to keep a record of your mileage per day and also your shift lengths. A shift of over 5 hours counts for £5 per day subsistence and over 10 hours counts for £10 per day. The mileage rate is 45p per mile if I remember correctly. Effectively you would probably be able to claim 20% of whatever amount you spend on travel and subsistence. It can add up, so it is worth it.