Increasing rent for a lodger more than once in any year?

I am a live-in landlord with have three lodgers in a small HMO in London. In the last few years, I have always charged a lot less than what I believed the market rate was for existing and new lodgers. However, with increasing costs, I can no longer easily afford to do this. In the last two months two lodgers who had both been renting here for several years left and I’ve taken on two new lodgers at a slightly higher rent level (but still paying below £500 a month) and there was such high demand and so many offers for the rooms, that I’m fairly sure that the actual market rent level is higher. I can also see much higher rents being advertised for similar rooms in similar properties/locations and according to the ONS the median level of room rent in this borough (to September 2020) is £718.

I’m wondering whether at the end of their six month agreements, I would be allowed to increase the rent again (providing the increase was not to a level exceeding the market rate) for any subsequent six month term, given that I have just increased the rent for my original lodger and that the two new lodgers would have only been renting here for six months. I would try to give them at least three months notice if I decided to do that and I wouldn’t do it until the start of any new agreement but I don’t know whether as a live-in landlord with lodgers in a small licensed HMO I might only be allowed to increase rent once a year ? While the rents are currently my only source of income and my costs have greatly increased, I don’t want to take any risk at all that I might break any regulations.