Opposite way around. We rent out our house after relocating. We're on a fixed term mortgage for another 2 years so we won't be putting the mortgage up at all. We make around £50 a month after costs and tax, which we save to cover any future mainainance costs such as a new boiler or just general upkeep.
Would not feel right at all to put it up just to earn more profit because we can, even though if the boiler does go or the roof needs repairing then the rent won't even cover our costs, but long term our tenants are still paying off our mortgage.
Once our fixed term comes to an end though, we will either have to sell or put the rent up because we can not afford to cover the gap between rental income and an increased mortgage.
So you'll have a mix of landlords: accidental or one-off landlords covering existing mortgages where increase in rent will depend on their mortgage increase, their own cost of living increases and their own greed; accidental or one-off landlords where there is no mortgage (often inherited) so rent increases will be based on their own cost of living increases or their greed; and landlords who do it as their income source/ business who will often have multiple properties, where rent increases will be either based on increased costs to their business (mainly interest rate rises if the properties are financed through mortgages or loans), or just their greed (I. E. Will put up rent because they can so that they can make more profit)
So long story short, increases will either be necessary to cover the landlord's increased cost to either maintain their current profit, or they may end up still earning less even after a rent increase. Or increases will just give the landlord more profit as they take advantage of the current shit-show