I would skip the agency and go direct to employer yelling them you’ve heard on the grapevine theres a vacancy. If they immediately say no then you know its crap from agency.
If yes then introduce yourself and point out that you’ve not worked for x agency for months so any release fees aren’t applicable, and just employing you direct would be a lot cheaper (by 1000s).
This is where you find out if the wages are crap too as they might pay X for agency, but less or PAYE on books.
Any hesitation on taking you on fulltime shows its likely to be crap between them and agency and you’d be dropped after the 13 weeks. Esp if agency route involves LTD or self employed as company is saving a ton on tax.
Wouldn’t jump until you have a fulltime job direct secured and even then I’d be cautious.