To Raise Rent or Not to Raise Rent?

Our tenants should, I think, expect rent to go up from time to time. Our costs do, and inflation does exist. I’m quite pleased that the house I own in Islingtopn let very quickly this time last year, even though this is just about the worst time for finding new tenants. And they accepted the full suggested price.
Well, it’s renewal time now. My agents did suggest a rent rise. So, I went by their advice and asked for a £50 per month increase. The rent is currently £1300 pcm. The tenants have come back and said that one wants to move out, but they have found someone to replace them. And could they keep the rent the same as it was? I asked the agents what they thought. One of them – and this particular one always seems to me to be a little anti-landlord – said it would be good to go with what the tenants want. I suspect his colleague may have suggested differently. The less senior colleague I spoke to wasn’t really very forthcoming. I did suggest that we built into the contract that the rent will go up by inflation rate next year. That may be beyond the normal procedures of this particular agent.
It is a difficult question. Why punish those who have been good tenants by putting up the rent? On the other hand, there are those extra costs to consider and would one really lose them for the sale of an extra £50 per month between three of them, when to move they would have all the problems of getting their deposit back, finding a new place and a deposit for that? Especially given that the new place will probably be as expensive, at least, as the one they’re leaving?