In simple terms, the question you are posing seems to be this:
"How should I invest my £100k prior to buying a house, if at all?"
Forget about the 3-year timeline for now. Assume you have £100k in the bank now, and are ready to buy a house. Would the bank prefer you to have a £300k mortgage on a £400k house? Or would they prefer you to have a £400k mortgage on a £400k house, + a rental unit you bought for £100k?
Remember that if you aren't buying a house, a bank would never lend you £300k at such (relatively) attractive terms. They would be afraid that you might lose your ability to make the monthly payments, and instead of earning a simple 5% interest on their loan, they would lose 100%. This is a large part of why credit card debt has such higher interest rates than mortgage rates: A mortgage allows the bank to place a lien on your house for 'security', which prevents you from purely 'walking away' from your obligations. A bank will assess your riskiness as a mortgage borrower based largely on its perceived ability to recoup any potential losses [if you fail to make future payments], by liquidating your house and making themselves whole again.
If you have £100k of 'equity' in your house from your initial down payment, then there is minimal risk to the bank of a total loss. As long as your home is worth > £300k [after liquidation costs!], your bank can't lose money on you.
If you have no in equity on your house [because you bought a different property in cash, beforehand], a £50k drop in value would mean that you would owe more on the house than it is worth, and might decide to stop making payments. Even if you used your rental flat as additional security for the mortgage, the complexity of the arrangement increases, and your proportional equity is lower, as well [if you bought the 100k flat, you would have property worth 500k and a 400k loan [20% equity], vs if you didn't buy the flat, you would have property worth 400k and a 300k loan [25% equity].
In addition, security against your principal residence is viewed more favourably by the banks, compared with security against a rental unit. A rental unit is purely financial, and therefore you might be shrewd about deciding to declare bankruptcy. However a home has emotional and practical elements that are considered likely to make you to continue fighting as hard as possible to make monthly payments on time.
You can add on as a further negative, that if you buy the flat first, it may drop in value before you ever even get the mortgage on your house - this highlights that if you are about to buy a house, holding any risky investments is not recommended, because you lack a long time-horizon to earn back any losses. Consider what would happen if you bought a flat for 100k, and your renter trashed the place and ran away - you would have additional costs to incur to bring it back to suitable condition, and the bank may not be able to count on the reliability of future rental income.