I rented for years. Some of the "rules" given strike me as a bit strange, for example asking the employer. There is no way my employer would speak to a landlord about me, two laws would be broken to start with.
You also have to beware of some landlords. One that I had didn't pay his mortgage for months. We got a letter telling us we'd be kicked out, complained to landlord ("Oh I've sorted it all now". Another letter giving the repossession hearing date and the locksmiths turned up. One of the guys I shared with (5 professional people) went to court to ask for some leeway (granted). We got no thank you from the landlord for saving him from repossession and strangely we didn't feel guilty about not giving a months notice of leaving.
I'm not sure what laws you are talking about, as it's fairly standard to ensure you work where you say you work, you earn what you say you earn, and you have been there as long as you say you have.
Any employer not prepared to give those details to one of the reputable credit checking agencies will be driving their employee into the rental black market, not the sort of company I'd want to work for.
I would not rent a property to anyone without those details, and nor would most reputable agents or landlords
Re repossessions, it does happen, its a tiny minority (about 2,000 properties a month in the UK, of which a single figure percentage are rented) and as you will appreciate its the last thing the bank, the landlord or the tenant want to happen. If the rent is (largely) covering the mortgage, then its quite common for the bank to take over the property with the tenants in situ, as a rented house is much better for all concerned than an empty one.