I presently own and have owned several 120v mig welders at any given time over the last 35 years. Stay away from off brand stuff and the name brand stuff sold at retail stores such as Home Depot and the like The name brand units sold therein are NOT the same equipment as available from Welding Supply dealers even when like capacity ratings; i.e., (120V/125 amp welders). The 120v commercial equipment costs maybe a $100.00 USD more than the retail equipment and worth every cent IMO. I use the Inner-Shield or Flux core gasless wire and the typical CO2\Argon gas wire. I've purchased used/abused many different name brand 120v welders; the best experience has been with Lincoln and Miller equipment. We use the welders commercially, predominantly for welding .065-.1875" HREW tubing in structural rail systems. They work GREAT with an ADEQUATE power supply, short heavy gauge chords or none is best.
Jason, Sorry if you got a wrong idea of wrong question, there are lots of welders here. As a business owner of a steel fabricating shop, I totally agree with Michael in the above statement. The cheap welders from harbor freight, and other discount tool stores will provide you a very disapointing results. A good used Lincoln, Miller, Esab, will provide great results. Even if you have to take to a welder repair place to get the proper parts and setup, you will not regret to get it fixed and set properly. They might give you some basic instructions, worth a lot. I could give many stories of people being disappointed with cheap welders and then using a name brand with a little training getting some worthy results. Flux core does not require gas, a little messier but giving good results.
If you only want the cheapest way to go, I highly recommend just forget welding, find another method.
I read the OP's post quite thoroughly and noted his location! As a matter of fact there are Home Depots in the UK... And I suggested "Hone Depot and the like". No Harbor freight, yet Amazon UK carries their products. That said my comments ring true matters not the location IMO. And YES Lincoln Welders are available in the UK too!