Phone up customer service and ask. Many airlines will do this. You don't have to give up your other card either.
I called AA and told them I was BA Gold. They ask for proof of your status (ie copy of your card, most recent miles statement) and more often than not will ask you to complete a challenge (ie fly a certain amount in a limited time) in order to get your matching status elsewhere. AA asked me to do 10,000 miles in 3 months to get Platinum status.
Its a good idea to do your homework first on your target airline.
www.fewmiles.net has some good tips for this.
My only caveat is that VS Silver isn't worth much: I quit flying VS 2 years ago by my silver card just never seems to expire. Also, you only need 1 premium class flight to get VS Silver. With most airlines you need quite a few (but will get better benefits once qualified) - ie lounge access which VS Silver doesn't get you.
If you are based in Athens (or can use an address there) I would recommend transferring your account there and applying with the Greece BA Executive Club. The tier status points requirements for continental EU residents are significantly easier than for UK residents, and BA may make an effort to steal a loyal flyer from VS. Also, you could get BA silver with just 3 1/2 x J-class return flights (http://members.shaw.ca/fewmiles/oneworld/chart.html).
[This message has been edited by whmere (edited 09-30-2002).]