How common is that in contracts and should I ask to have this removed?

[Lance]

This protects the agent's revenue stream so not a chance they will remove it.

It is actually unenforceable in most cases as it's far too generic and 12 months is too long. No chance that will stand up in court. Handcuffs have to be fair and reasonable that that one is not. Doesn't really help you knowing that because the agent will try pull it and you might have to get lawyered up to defend it.

That said... Does it even make sense? Looks very badly written to me but them I'm a bit crap at legalese.

your legalese may be crap, but not as crap as whoever wrote that clause. And they charged over £200 an hour!!!

[MrButton]

I suspect the OP replaced the agency name with “Agency”

[fidot]

Unless the services are defined as being for this one client on this specific project, i personally wouldn't agree to the clause.
As has been said these clauses are written to protect the agency's revenue stream and that shouldn't be an issue normally. However this clause seems to be saying the op can't work anywhere other than through this agency.