Toilet door stuck - help

[Rhubardandcustard]

No urgent as thankfully nobody was in there.

The handle has been loose for sometime and uve been meaning to get round to it for awhile but am single working parent and just haven't got round to it!

Also am limited on tools as round this time of the year my shed door gets stuck and I have to wait until dryer warmer weather to access it again.

I have a couple of screwdrivers in the house and that's all pliers etc all stuck in shed.
I've taken off the screws from around the plate, but that's all, the plate won't come off, so I can't get to the spindle. There's not enough room on the door frame to get a plastic card or similar to the lock.
Any ideas before I have to call out an expensive locksmith? It's Christmas and money is tight so very grateful for any suggestions.