If your rear derailleur is a Sora RD-R3000, then a new 11-34t cassette will fit. Probably also need a new chain. Under £40 for parts, so shouldn't be excessively pricey at lbs. But would make a hell of a difference.
No because you need a 9 speed one no?
And you'll need a new chain and potentially a long cage derailleur
Where did you find the cassette for only £15 (and is it actually available?)
I've recently swapped out a 11-28T 9 spd cassette for an 11-34T cassette with a 26/36/48 triple on the front but my Tiagra rear changer didn't have the capacity and so I had to get a new rear changer too - I got the Sora RD-R3000, so if the OP has that model, it will handle the capacity fine.
I would definitely recommend getting the chain whip and cassette tool and doing the job yourself (you will also need a chain-tool as you will need a new chain - wear aside, the current one will most likely be too short). The ability to do the necessary gear adjustment is something that you will need to maintain your bike anyway and the rest of the work is not difficult - it will stand you in good stead for any future work/maintenance (possibly including emergency roadside repairs).
EDIT: - my rear changer is Sora RD-R3000
GS - GS indicates medium length cage. My old Tiagra was GS too but the capacity was different iirc.