OP, this web site is well worth a visit: British Baby Names.
You can download lists of how popular names were in 2011 from here: www.ons.gov.uk/ons/publications/re-reference-tables.html?edition=tcm%3A77-266770
And you may want to look at names.darkgreener.com as well, which reveals trends.
Rowan is a fairly common (#135) boys' name. It was given to 473 baby boys last year. It is, however, well-established as a girls' name as well and was given to 69 baby girls last year. The most common namesakes in the UK are male - Rowans Atkinson and Williams - so you may find that people occasionally incorrectly assuming that she is a boy from reading her name.
Weston is a really unusual name in England and Wales; it was given to just 4 boys in 2011. (Wesley was given to 64 and Westley to 5.) It is easy to pronounce and sounds more familiar than it actually is so I would not be concerned. It does sound very American but he is American and I think a lot of Brits would love to be able to 'get away with' naming their sons names like Weston!
Hadley is also a very unusual name in England and Wales, given to only 10 girls in 2011 and 47 boys.
Harry is the most popular boys' name in England and Wales and Harrison is also well in the top 50 at number 37 (given to 2,122 boys).
Finn ranks at 136 (469 boys) but Finley is at number 34 (2,245) and Finlay at number 66 (967).
Asher was given to 89 boys, ranking as the joint 436th most popular boys' name with Stefan.
Beatrice is quite common, ranking at 126 in 2011 (having been given to 460 girls).
Winifred is unusual, given to only 22 girls (placing it as the joint 1374th most popular name along with choices such as Viola, Yasmeen, Roxanna, Rochelle, Suki, and Seraphina).
As your children are named Rowan and Weston, I would be inclined to pick names similar in style for this baby. I would therefore not use Beatrice or Winifred, as lovely as they are, or Finn, Harrison or Asher as they are either stylistically poles apart or else massively more popular than your current picks. Hadley works the best with your other two choices.