At Heathrow there is no Qantas lounge, however you will get into the BA business class lounge with either Qantas club or Qantas gold.
Barcelona is a little more tricky. There BA uses a 3rd party lounge. This usually means access is only granted to Club Europe (business class) and BA status holders, meaning Qantas club and Qantas Gold is not accepted (I got caught out with this in Dublin a few times when BA used to fly there). Having said that though if, as I suspect the 3rd party lounge that BA uses is the Iberia lounge, then OneWorld Sapphire (Qantas gold) will get your hubby and you in, but Qantas club certainly won't. And if the lounge is not Iberia then even Qantas gold will not be accepted, but always worth a try.
Below is a link to all BA lounges showing which ones are BA and which are 3rd party. Pity BA doesn't say which lounges in Europe are operated by other OneWorld partners like it does in Asia and Australia.
British Airways - Lounge locations