Some of my thoughts:
A) Don't take what estate agents are saying for granted. They work for vendors to sell their houses and earn money from the sales so what they say depends on how they judge the situation in order to trick you to make offers. Of course it varies and some agents may well tell you 100% truth but stick to your own research, as you've done for finding out the previous prices and throw the evidences to the face of agents' and then see how they react. The more you play this game, the more you will find out estate agents are NOT your friend.

Always think of how resellable a house is, even if you have no plan to move in the near future. Things do change and when you come to the stage of reselling, you might regret your decision so better make a wise decision when buying. 3 bed is generally more expensive than 2 bed and in your case, I'd go for the 3 bed if your budget is not so tight and there is no other problem with the 3 bed as 30K is not a huge amount differietiating two properties. According to their prices, either the 2 bed is top-end or the 3 bed is at bottom or, one of them is over or under priced.
C) You of course can make 2 offers but don't do that just now. You can express your interests in both properties and show that strongly to the agent you are getting in touch. The purpose of that is to show you are a serious buyer and make the agent aware that you're going to make decision which creates a competition. At the end of day, you can only buy one property and the vendor of the other one will be disappointed. To avoid disappointment, the two vendors have to act quickly to win you. When you are buying, the worst case is someone else is also chasing the same property you are interested in, and the best case is more than one vendors want to sell house to you. If both properties are from same agency, you are in a great position to play this game and let them do something special for you.
And finally as you've concentrated your search to only 2 properties, this webpage may be quite helpful for you:
http://www.moneysavingexpert.com/mortgages/free-house-prices