Moving house - Estate agents' conflict of interest

Chatting to the estate agent when we were looking at the bungalow we are interested in, it turns out that there is another woman (Woman A) interested. Anyway, it turns out that Woman A is so keen she has made a decision to put her house on the market as she hopes to buy this bungalow. The bit that interested me is that she is putting it on the market with the same Estate Agents.

This got me thinking about conflicts of interest and who the estate agent is really working for if Woman A makes an offer to buy the bungalow: the buyer or the seller of the bungalow?

Furthermore, when I do come to sell I won't use the same agent. And what happens if I make an offer: will the estate agent think he might lose the opportunity to sell Woman A's house fearing she might take it off the market? If he does will he put my offer forward with any vigour?

I can see I am going to be in for a fraught time on this one and will have to keep my eye on this Estate Agent. Fortunately it turns out we know the owner of the bungalow through a mutual friend so will get wind of any shenanigans.