Being Evicted Is Not A Crime
It is not a crime to be evicted. So, you will not get a criminal record if you fail to pay your rent and are evicted. Failing to pay rent is merely a breach of contract, and eviction is a remedy for this breach of contract.
Damage To Your Credit Rating
Being evicted will absolutely hurt your credit rating, however.
In the U.S., a bad credit rating can be considered by prospective employers and for many other purposes (e.g. as grounds to charge you higher insurance premiums, or to refuse to rent property to you, or to refuse to extend you credit).
I am not familiar with all of the purposes for which a credit rating may be legally used in the U.K. and that would probably need to be the subject of a separate question in any case. At a minimum, a bad credit rating makes it harder to get loans in the future. For example, an eviction could result in your application for a mortgage when you want to buy a house being denied, or could cause you to pay a much higher interest rate on a car loan.
Other Negative Consequences Of An Eviction
There are other negative consequences of being evicted in addition to harm to your credit rating, which may seem obvious but also bear mentioning.
These consequences are all very good reasons to voluntarily leave the premises from which your landlord is trying to evict you and to move to a new residence of some kind before a court order evicting you is carried out if it is at all possible to do so.
First, if you don't have a place to live immediately, when you are evicted, you become homeless and being homeless is not a good thing. The U.K. has a decent safety net, so eventually you may be able to find public housing if you are evicted, but that often doesn't happen immediately, and in the meantime, you are literally on the street.
Even if you can't find any place else that you can afford to rent, you can try to find friends and family that can take you in temporarily, attempt to locate places you can legally camp for a while, and can save up enough money to pay for a motel for a few days at least while you are looking for alternative places to live.
Your Stuff Is Tossed On The Street
Second, if your stuff is in the property you are being evicted from, then when you are evicted, your stuff will be tossed out on the street and in all likelihood it will be damaged or stolen or otherwise lost.
Among the things that can be lost or damaged in an eviction are documents that you need which are hard to replace like birth certificates, passports, professional licenses, college applications, report cards for children, health records, financial records, family photos, immigration documents, etc.
Even if you can't afford to rent a new place, you can avoid this harm to your property by putting as much of it as you can in a storage unit. At a minimum, try to find some place (maybe friends or family or work) where you can store your most valuable property before you are evicted.
Lost Security Deposits And Money Damages
Third, if you are evicted, you will almost certainly lose your security deposit and will probably also have a money judgment entered against you by the landlord for any amounts owed to the landlord for damage to the property, back rent, late fees, interest, lost rent while the property is rerented, attorneys' fees, court costs, etc. to the extent that it exceeds the security deposit which it usually will. This money judgment will further hurt your credit rating and could cause your wages and bank accounts to be garnished and your cars and/or other personal property to be seized to collect this debt.
Usually people are evicted because they can't afford to pay rent, so there are limits to what you can do to prevent this, but at a minimum, try not to damage the premises which can result in additional amounts owed.
Disruption Of Postal Service
Fourth, until you can get change of address arrangements made, you will not receive any postal service, including bills you owe on loans and credit cards (or even worse, demands to respond to small claims court lawsuits up to 100,000 pounds). Failing to pay these bills or to respond to notices can lead to more damage to your credit, late payment penalties, default judgments in court cases, and other problems like disrupted efforts to apply to universities or to meet requirements to obtain scholarships.
You can avoid this by obtaining a post office box and redirecting your mail there before you vacate the premises.