Slipping wheel

I have just built up and riden (for the first time) my Brian Rourke roady.

Here's the issue, as soon as I drop from the big ring to the small ring the rear wheel is pulled forward (drive side) and rubs on the opposite chain stay (non-drive). This was obviously an issue had before as there are tyre rub marks on that side.
I'm beginning to think that it may be, the chrome drop-outs that are causing the slip? It just baffles us that it doesn't happen on the big ring.

Do I take my junior hacksaw to the drop-out and get some grooves in there?

Quick release skewers?

The big ring / small ring difference is most likely due to the fact that the pedalling force is being applied to the wheel in a slightly different direction because of the different chainline.

more likely to be the torque difference between big and little rings

New Chain?

Quick release skewers?

Yeah QR. Most probably cheapo's.

New Chain?

Brand new chain

most likely the axle is protruding beyond the dropout. so the QR is clamping against the dropout a little and clamping against the axle too. you dont want it clamping against the axle, just the frame.

FIX: big washer around the axle. do it on the side it slips. bit of a bodge but its a fix

otherwise file the axle down or space it out more.

i suspect thats the problem, often happens.

This used to happen to mine a lot. Apparently some skewers are designed for vertical drops so dont apply as much pressure as other Qr skewers which were designed to stop slippage as well. I just seriously tightened my skewers and prepared myself to het my hubs serviced more often.

Some titanium drop outs have this problem, it's usually solved by switching skewers.

Cheers everyone. I'm gunna try some of the suggested fixes over the coming week. Will keep updated!

It turns out the QR heads were made out of cheese, so have changed those which has resolved the problem!