For a Saas trading as a sole trader does not make much sense to me, as you are personally responsible, not a company. And you'll likely want to move to a company sooner than later, anyway.
Dude asked for the leanest version, that'd be it — I'd go sole trader and have it legal, all while seeing whether the SaaS lifts itself off the ground or not
It's arguably not the leanest, then.
IMHO, with payments processing to be setup and legal liabilities it is a good idea to completely separate that from your personal finances. On a more subjective note, it also projects a more profesional image.
It would be good if Jackypot would reply to comments so we could understand what is his issue with setting up a company.
Note, btw that it is not accurate to say that for a sole trader profits up to £12.5k are untaxed as this is the "personal allowance": This amount relates to your personal income as a whole.