Another way of looking at this is to ask what kind of work are you likely to be procuring for yourself anyway (because the vast majority of jobbing actors *are* finding 80% of their own work at any given time)?
If it is extremely high level, well paying work (and thus paid at proper Equity rate, or BSF rates, with a usage contract for screen and so on), then a)it would be churlish *not* to offer the agent a percentage of any work you secure, particularly if you are aiming to keep the relationship with the agent on an even keel and b) more importantly, it shouldn't matter *who* sourced the work - the agency percentage will have already been taken into consideration as part of the pay deal, as it will be assumed most actors who are being employed will also be represented by intermediary negotiating parties!
When you are sourcing work that is paying below rate, you will tend to find there are three types of reaction from agents: a) They will be the sort of agent who do not want you working on this type of material anyway - as it offers them nothing remunerative and your involvement with it precludes availability - so they will aim to dissuade you from accepting it altogether
b) They will be (for the jobbing actor) what is probably the best type of agent - willing to waive levelling a percentage on any work that is not being paid above a threshold level, and yet still happy enough for you to undertake it, given that you keep them well informed of what you are doing (the economics of this arrangement is fairly obvious: if you earn £100 for a screen job, and the agent gets to level 20% on your screen work, then, in seriousness, is going to the trouble of winning back £20 from this job worth it to them? It's unlikely to be, whereas if you are 'holding out' on a job that has just netted you £25,000 in a day because you 'sourced it yourself', there may be more of an issue!
c) They are the type of agents who wish to handcuff you to a deal agreeing that you will have a percentage taken from all work you do for money regardless of the source of landing the work - and, more importantly, in my view, regardless of how much you are actually being paid for it, whether an agent's fee has been calculated into the earnings and so on. I wouldn't personally sign a contract on that basis, because I see a good working relationship with the agent as one of negotiation between yourself and the agent, and lacking any kind of adaptability on a project by project basis tends to ruin an actor/agent relationship. In my opinion, some material (regardless of who sourced is) is fair to take commission from, and some (regardless of who sourced it) isn't. The better the relationship with the agent, and the freer you are from any written contract on this basis, the more you will be able to negotiate with your agent over the question of payment for each job case by case.