Cost would be renewing the sim card each month. So GiffGaff for example would be £18 a month for 6GB of data. If you use less then you could use a cheaper package, say 4GB for £15 a month.
GiffGaff is O2 and is pretty good for me at the moment. Notice no difference from when I was on 02.
If you have an spare phone then you can try it at almost no cost. Get a sim (free) activate it (£10 for some data) and create a wifi network with that phone. That becomes your source of internet for the test. If it works then a) you could leave it running like that b) get a proper router and do it "right".
Do you have any visibility of what you currently use in terms of data? Does BT tell you that? I know Virgin will if you call them up.