Yes, you will need to include the property income pages in your self-assessment tax return if you already file one.
It is possible that if HMRC is unaware of your income (apart from tax-exempt savings and ISA’s), not declaring that income could be considered evasion, if it is later discovered.

it is likely that you will have to pay stamp duty on the purchase. The exact amount that you will need to pay is determined by the value of the purchase and whether you already own a home. The Government has issued a useful stamp duty calculator that you can use to determine the amount payable

Whilst it's not technically called capital gains tax, you have to pay tax on the gain when you sell a property from a limited company. When you sell a property through a limited company you pay corporation tax on the gain. You're not entitled to use your capital gains tax-free allowance here, however for higher rate tax payers the overall rate of tax can be lower via a limited company.

It could be possible, depending on the number of properties and their amounts, that VAT may apply.

Greater London has a planning restriction that affects short-term rentals. In most cases, it’s considered a “change of use” to use your residential premises as temporary sleeping accommodation.
The Deregulation Act of 2015 introduced an exception that allows you to use residential premises for short-term rental for 90 or fewer nights in a calendar year. This is known as the “90 night rule”.