I run an original 70 plate on my car too and keep the current tag under the passenger seat...
Was stopped once by law enforcement in another car I was running a vintage tag on. I forget what the tag was but it was an obscure combination that's now currently reserved for commercial vehicles only and my 240z didn't fit the bill. Needless to say I got to spend some quality time on the side of the road while he looked it up. In the end there was no problem, but it certainly slowed me down a bit.