Does Bank Manager's discretion still exist in Mortgage Lending

It is important to differentiate between corporate and governmental policies. It is unlikely that the governmental policies are that draconian. However, it is plausible that corporate policies are exactly that. If customer A does not meet these guidelines, then the answer is "No".

There is another possibility, if you have already been turned down. Perhaps the banker looked over your financials and their discretion said "no". They then might blame the "no" on some unseen boogie man to avoid conflict and perhaps earn your business on a more affordable property.

Your best bet in these matters are to establish a good working relationship with a smaller bank. You want the kind of culture where a loan officer could have a conversation with the VP in charge of lending if not the CEO of the bank. That loan officer can then make your case to a decision maker that can override policies.

Please also consider that the bankers may be correct, and this home is beyond your means at this time. I plugged some numbers into an online UK mortgage calculator and the metrics say I can borrow quite a bit considering the numbers that I entered. In fact it was way more than I would be comfortable borrowing.

House fever is a real thing, but you will get over it.

Pete B. has provided a practical answer. I'm answering separately to address an interesting point you brought up:

(Alternatively ... is this all bound by regulation now, so that the concept is legally impossible now?)

In the strictest "regulatory" sense, in most countries, there are basic banking regulations that strongly deter making loans to people who can't afford them (especially real estate loans). For instance, in most banking systems, lenders are responsible for maintaining reserves based on the risk of their loan portfolio - those reserves have to be calculated based on "putting numbers into a formula" in order to level the playing field and allow aggregation - they can't be calculated based on what the branch manager thinks about Farmer Joe who they've known since they were kids. A lender who makes a lot of loans that the formula says is risky, even if they personally don't think the loans are risky, is going to have to carry a lot more reserves. And there may be regulatory pressure on them more generally which makes their operation expensive to the point that it doesn't make sense to make those loans in the first place. Thus, even though there may technically be some leeway in the decision making, the lender's hands may be tied.

If we step beyond regulation, and look at the way most mortgage products operate in most banking systems, there are many other pressures that also serve to deter or downright stop "risky" lending.

For instance, in many countries, mortgages that are deemed more risky will have requirements for insurance of some type, to protect the lender or the entity backing the mortgage. Often, this means the decisions about what the most risky loan possible could be are in the hands of the insurer, not the bank. So, even if a bank would be happy to lend you the money, they may not be able to insure your loan, because the insurer won't underwrite you.

Similarly, in many countries, mortgage products are either backed by a central bank or other central entity, and/or they are typically sold to banks that specialize in carrying real estate loans. Again, this doesn't inherently mean there is no leeway in the decision making, but if a bank is not backing their own mortgages, or they intend to sell the mortgages they write, once again we end up in a situation where a third party is responsible for making the decision.