Thinking about your job Lonsdale, I suggest that you do exactly as CHJ has drawn but instead of tapping and using a bolt, you rivet it. This assumes that A) the plate doesn't have to rotate on the bar, and B) a permanent fix is OK.
If the plate is already tapped, drill the thread out to clear it, then countersink, but ideally use a 100 degree c/s instead of the usual 90 degree (these are common in the aircraft industry and can be bought from Snap On amongst others. The reason for 100 is because although it's ss, your plate is only 2.5 mm thick and this will make a much better flush head that won't distort the plate or break it in use).
Choose, ideally a steel c/s head rivet, or a hard "aircraft alloy" 7000 series rivet, NOT a "standard" pop rivet, and make sure it's a tight fit in the hole. Cut off the length so that when entered into the hole it's between 2 and 3 times the rivet dia above the combined plate and bar. If you're used to riveting you can form the head with only a ball pein hammer, but best is probably to buy a rivet snap and dolly to at least start & finish the head forming on the other side.
HTH.
But if the pieces are small you can send them both to me and I'll do the whole job for you as I have all the rivets and gear necessary. Your only cost would be 2 ways post, but unfortunately the Swiss PO are rather (to say the least) ridiculously expensive, sorry. The job'll take about 10 mins!
Alternatively, IF I can find it, I can send you a scan of the appropriate pages of my initial apprenticeship training manual - I think I've still got it somewhere - so you can have a go yourself - assuming you haven't already learnt hand riveting. It's quite easy once you get the knack, and really useful.