then I'd suggest taking it to any high street clothing repair shop; it looks like the bungee cord is fixed at each end of the sleeve. All you'd need to do is unpick the bar tacking that hold the cord in place, thread in some new bungee cord (you might have to supply that; plenty of online and highstreet sources), and then bar tack the ends in place again.
You could even do it yourself, by hand, if necessary.
Thanks for your replies. The guys at Outside pointed me up the road (literally) to Alpkit who have a fully kitted out repair room. Picked up my repaired sack today and it looks like they’ve done a great job - for £5!