I've never been asked for ID in a hotel, and I've stayed in them more times than I can remember because of business trips. Just go to reception, tell the receptionist your name, he or she looks it up, sees "oh yes, we have a reservation for you", tells you your room number and gives you the key, and shows you where the lift is. They work on the basis that it's not likely anyone else knows you booked a room there, so it's 99% certain you ARE who you say you are.
But it would be VERY wise to check first if the hotel allows guests of your age. The usual problem with under 18s is that you can't make a legal contract, so if you leave without paying, they can't sue you. (Same reason you can have a debit card but not a credit card, as a bank isn't going to let you borrow money if it has any sense. It can't sue you if you don't pay it back!) That's not a problem if you paid in advance, of course. But they still might not be keen on taking children on their own. The last thing you want is to be stranded without beds to sleep in. It will sound better if Mum calls the hotel and checks this for you.
Talking of contracts, same thing if you actually get the job (and good luck with it!) There will be a contract to be signed and Mum will have to sign it because you aren't old enough.
There are several things that can go horribly wrong here:
1) You cannot legally do a "modelling" job if you are under 18 without your parent's or guardian's permission. The agency who employed you would be in versy serious trouble and you would also damage your own future chances because no reputable employer would take on someone who lied and deceived a previous one.
2) Most hotels will not accept a solo guest under 18 without them being sponsored and vouched for by an adult. This is self-protection by the hotel because by accepting you as guests they would be taking on repsonsibility for you and, your safety and behaviour, at least while on the premises; and I cannot think of any hotel that would do that.
3) By paying with a debit card you will be reducing your bank account balance in a way that could quicky become serious. The bank will probably not entertain giving you an overdraft because of difficulties making you pay it back.. So you may find yourself out of money very quickly. This will happen rapidly if you stay at a hotel which is decent.
If you find a very cheap hotel or hostel, especially one in a back street or industrial estate that is deserted at night, then you also are taking on very serious risk of personal danger - attacks, robberies and rapes DO happen.
If your mother has any sense of proper care for you then she must travel with you and check you into a decent and safe place herself. She must also make sure that she signs the proper consent form with the modelling agency or employer. These are the very least things that a caring parent must do to prevent it all turning bad. Saying that "family members will check up..." is NOT GOOD ENOUGH. You must be properly settled at the very beginning of this enterprise.
The consequences of letting you off on your own and things not working are too serious to mess about with. If you lost your money (or worse) then your mother would also be in serious trouble with the law, and no "she must work" excuses will help her. The law takes parenting seriously and she must accept her responsibility - and you two have a duty to help her do it properly.
No hotel will allow a 15 and a 16 year old to stay without an adult. It's linked to insurance and fire regulations.
I think your lesser concern is a hotel room most will not accept two girls one aged 16yr the other 15yrs as they are not legally responsible and legally is the key word. NO modeling organisation who are real will accept under 18yr old without their parents present ( LEGALLY) as they can't in law sign a contract so think again.
Call the hotel and find out first. Better to know ahead of time than be turned away.
Premier Inn should take 16 year olds. Your Mum needs to phone and check first for you.
You can not pursue a modelling job at your age without an adult present. No employer worth anything will see two under age girls without an adult present.
And your mother is ok with this? Wow. just wow.