Is this a dog rose?

This is a very old rose called Complicata, or R. Gallica Complicata. Needs to lean against something as it grows, has lax stems. The dog rose you mean is usually verypale pink and very vigorous. It's the rugosa root stock of most hybrid modern roses

Thank you so much. Is it possible to buy this rose from a garden centre? I think I may have managed this ages ago but had to leave them behind in a move...unless it wasn't this exact type. I am so grateful for your help!

There are rose suppliers on line, but I'd wait till winter and get it bare root if it's going to be delivered by mail. Otherwise, ring round your local garden centres, see if they can get you one, or contact the British on line suppliers who have garden centres and speak to them, if you can't find it on line. RHS at Wisley could be worth a try - they have a good garden centre there and the staff are very helpful on the phone. At least you know what to ask for! think the RHS website has a plantfinder facility too.