Thanks all! Helpful suggestions all round.
Battery not fully dead, I should clarify. The electrics work, but trying to start the car makes that horrid wrenching noise that says the battery is too low. Effectively it just slowly discharged over time, which is totally my fault (annoyingly!) - it's been a very very busy time for me, and the car simply hasn't been for much at all in months, including not once in the last 5 weeks. This has included a few very cold snaps up here in Edinburgh...!
So my secondary concern is getting the car back to good shape for a summer of heavy use, after sitting for so long. Fuel injector cleaner with the next tank of fuel, and will give her a full service in 6 weeks when I'm moved out of Edinburgh and back to the countryside. Not to hijack my own thread, but any great tips on that are all welcome.