Laptop Repair/Soldering Iron use

Hi all, my laptop hasn't been charging properly recently so I've taken it apart to find that the power jack had only one connection still soldered in place.

I've been to a few electronics shops on green lanes who have said they only do "the full works" or words to that effect and quoted between £50 and £70.

If I had access to a soldering iron it would be a matter of minutes work.

Anyone got any recommendations for a reputable electronics repair shop or is willing to do a tiny bit of soldering/let me borrow their iron?