You can do all of these things as an individual, and you would report the income / expenditure as part self-employed (self-assessment) return to HMRC.
There may be tax advantages of setting up an LtdCo, but you'd have to talk to an accountant about that. However getting a buy-to-let loan as a new LtdCo may be a dissuading factor for LtdCo. It depends on your situation and other factors.
Don't forget that there is a potential future liability to capital gains tax on your existing house (when it ceases to be your principal private residence) if property prices continue to rise, so you will need to establish a fix on the value of your house at the point you move out of it