As Scott says, you can run 2.5mm rods off a 13A socket, no bother. My little old buzzbox only goes up to 125 Amps, but will run 2.5 easily, so long as there's a minute or two pause between rods or runs, which there usually is in hobby welding.
Incidentally I used to have a SIP 160 Amp, and this tended to knock out the breaker or blow the 13A plug fuse running 3.2mm rods; just had a higher inrush current than the 125 Amp m/c, I guess. But it would run 2.5's without blowing fuses unless I stuck a rod.
The Esab Buddy Arc 145 is an inexpensive choice & is coming from a reputable manufacturer. Package price will include leads. Tech wise it will require a 16A fuse for working at top wack but below that should be OK on a 13A supply. Will run 3.2mm electrodes & have been very reliable for us, can't recall a single problem with them. Currently on offer.