Most scrap yards will have a full size weighbridge that has to be accurately calibrated, by law. The only risk you run is getting shards of metal in your tyres. Lots of factories, especially ones with tankers and bulk trailers coming in and out will have a weighbridge by the security lodge. Just pull in and ask for a printout of your cars weight!
Thanks both for your replies - I have an idea about a local factory where I might ask. I'll post up the result when I have it. MGT are great but I hope it'll be a few months before it needs their attention again