I have a BT Wireless home hub and frequently lag when playing games on my PC. The games I lag on aren't particularly demanding and quite are few are even old games. Should I change service provider or invest in an ethernet cable?
Invest in an Ethernet cable anyway, even if you do leave.
The cause could be bufferbloat. Investing in a 3rd party router with good QOS might help
buffer bloat is only an issue when your connection is fully saturated. Buffer bloat is a non issue if you're only playing a game and streaming using 1MB/s of your 4MB/s for example.
If you're getting lag spikes and the only thing that's using your connection is a game, then buffer bloat is a non issue.