I think you need to be clearer on what you mean by gazump.
You say the friend has made an offer, but not whether the offer has been accepted. If it has, then offering more in hopes that the seller will break the agreement in favour of you is really horrible. It's so dishonourable, I know estate agents who will tell buyers they disapprove. Do you really want lower morals than an estate agent would display towards strangers, when you are talking about a friend? And it may not just be one friendship harmed, in that scenario, either, because they'd be unlikely not to tell people about it and quite honestly, I'd not feel the same about someone able to do that to someone they were meant to care for, either.
It's knottier if you don't mean gazumping at all, but instead a competing offer. That's socially very awkward, but not wrong per se. We all bid what we can afford for the home we want. That's how house buying works in a hot market, and isn't gazumping. In that situation, I'd consider how much the friendship means, because you'd be likely to lose it, fair or not. So much emotion is tied up in housing. But if it's still on the market, then it's not wrong, no. And realistically, it could be that neither of you have the winning bid, because if you both love it, and the seller is yet to accept your friend's bid, then probably so will other people.
Finally, in practical terms, I'd also consider how rare such a house is likely to be. I mean, this is a lovely area, but unless you are talking crazy money, you're presumably talking about the sort of terrace that is commonplace. If so, then you are unlikely to find this is a once in a lifetime chance because the housing stock is fairly homogenous. As a child, I always knew the layout of my friends' houses, because it was my own. Most in the Honeywell catchment were. Is this house really worth the social consequences, quite apart from the moral issue?