I am painting some wooden internal window sills and skirting boards, and a yellow-brown stain is showing through the paint. From the answers to What are the brown stains showing through my white paint? and Primed wood and painted with white paint but looks yellow. Why and how to fix?, it looks like it is probably tannin leaching out of the wood and through the paint. I'd like to know how best to fix the problem, ideally without having to sand back to the bare wood and start again.
I'm not sure what type of wood it is, but it was a reddish colour, and previously covered with a dark red-coloured varnish. The varnish has been scraped off, then sanded down and primed with white 'Valspar Wood Primer & Undercoat'. The stain was quickly visible through the primer, so a day or so later, a second layer of primer was applied before painting with white 'Dulux Quick Dry Satinwood for Wood and Metal'. While this initially looked OK, the stain is now starting to show through again.
The answers to the questions linked above talked about using primers to stop staining in the first place, but didn't really discuss how to make good stains that were coming through. After all the painting I've done so far, I'm not keen to sand it back to bare wood and start again with a different primer. Is there anything I can apply on top of the satinwood paint to stop the tannin coming out before a final coat? Recommendations for products I can get in the UK would be welcome.