Looking for a pump with a bracket to fit on CX frame and able to get up around 80 – 90 psi without too much effort ! Oh and under £20 would be perfect ! 😀

Not sure if you can get them for under £20 anywhere but I like the lezyne alloy ones. I use a high volume (“alloy drive”) one for mtb and CX (running 40-50psi) and a “pressure drive” one for road. I guess you’d be wanting the pressure one, 80-90psi? you running road tyres? They come with bottle cage mounts.
The small one is OK for road tyres and bunging in your pocket but if you’re going frame mount and bigger tyres then probably get the medium.
linky to pressure small