Will I receive a 30-day visa exemption stamp upon re-entering Thailand after visiting Laos with a UK passport?

If you're NOT gonna be here for the 60 days you get on the tourist visa (as you say you might go to Lao 4 weeks after arriving here, just come here without any visa and enter on a free 30 day visa exempt entry and know you can extend that for 30 more days once for 1900baht at the immigration office if you needed to .

As far as you re-entering thailand if you do go to lao, you will get another 30 day entry stamp when you come back in.