If the source of income is UK and the work is performed in the UK, and if the person(s) doing the work is (are) UK-resident (never mind ordinarily resident) then you have (1) a permanent establishment, (2) probably IR35 issues, (3) shadow director issues.
The only conceivable benefits that I could envisage are: (1) deduction for foreign pension, at least foreign state pension (a very arcane area), (2) (perhaps) avoidance of the need to publish accounts (whether you need to register the company as a foreign company doing business in England/Wales and (3) ease of staying below the radar (this verges on tax evasion, be careful).
The issue comes up constantly in France, where (especially in the old days when English companies weren't taxed if they did no business in England) every hairdresser and baker wanted to incorporate a company in England and run his/her shop in France through it. There's a lot of stuff on misc.droit.fr (in French) on the subject.
There may be VAT complications or benefits. If the company is below the VAT threshold that might be a savings. I have not been following the issue of "related companies" and "collapsible corporations" set up by related parties to avoid VAT registration; there must be rules to regulate that and they might be unenforceable against a foreign company. On the other hand, you are not foreign, and they can always assess you for whatever they like.