A few random uninformed thoughts to consider.
I could not quite make out if you had a hotspot device already or if you were just using your phone in hotspot mode.
If you do have a hotspot mifi device you could get an access point with client mode support. Such as many of the Tp-link ones, often available for ten pounds on ebay. This would connect to your hotspot by wifi and send the signal out of an ethernet cable into your homeplugs and thus your sky router which you could use as an access point. You would then have two access points in the house both using the same internet. However adding more wireless steps does tend to cut the speed. Its a bit crude and inelegant with lots of bits but would basically work I think. I did something similar when my phone line was broken and my mifi was wifi only and it basically worked.
Alternatively you could go with three homefi service which is £24 a month for 40gb but if you sign up for a year you get a free mifi router with one ethernet socket that would work for you. Or a 30 day contract would cost £60 for the router. I don't know for sure if it is unlocked but I would suspect it is. Obviously check there is a good three signal first.
Anyway there are two more options for you to consider in more depth.