Air in system - any more ways to get it out

I live in a flat with a small boiler and the hot water tank on about the same level separately. The system has two automatic air vents, one by the boiler and one next to the tank. The pilot light kept blowing out (due to overheating cut out) which the plumber said was due to an airlock. He managed to force the air out of the system, but since then it's been getting worse again. The air vent by the boiler was letting out more and more air when we relit the pilot light each morning before it started heating properly. I found one radiator was cold at the top so tried to bleed it but didn't turn the heating off first (stupid!) so it sucked more into the system. Since then it has done nothing but blow lots of air out of the vent when we relight it, before going out. I thought this would eventually fix the problem by getting the air out of the system but it is getting worse if anything and I am worried about heating a dry boiler if it is just full of air. The radiators have no air in and there is no flow getting round to them and no air came out of the pump when I tried the bleed valve there, just a tiny trickle of water. We have the plumber coming again on Monday, but in the meantime is there anything at all that I can do to get any more air out of the system? Is there anything other than a lot of air that could be causing these symptoms (I suspect we have that black gunk that is mentioned a lot, but I can leave that for the plumber to deal with). Thanks for your help.

Your making matters worse, stop taking air out and try putting some water into the system.

I didn't think it was a sealed system. Doesn't the water go in automatically? If not, how can I put some more in? Thanks.

Should I do the cold tap to hot tap link suggested in previous posts?

No, don't do that.

Do you have a sealed system or gravity.

Make, model of boiler.

Economist MYSON Boiler.

Not a sealed system, the hot water tank has a cold feed tank above it.

You should have another small five gallon tank for feed and expansion on your heating system, check it has water.

Sorry for being thick, but I can only find a small boiler in the kitchen and a hot water tank with another smaller tank above it which I presumed was the cold water feed (this is the one with the ballcock in it and has lots of water) in the cupboard. Thanks ever so much for your help (especially for stopping me making mistakes) but I think I'm out of my depth here. New plan - buy a heater from Argos and make do till the plumber comes on Monday!

Sounds good.