Yes. They won't give you supplements/injections if you're in the "normal" ranges, however unrealistically low those are on the NHS.
From what you're saying, coeliac seems likely then.
The below is what worked for me, but my issue really was severely symptomatically low B12 & low ferritin, just not so horrifically low that they would treat it. So please do your own research, cos I don't have coeliac.
Liquid B12, as a mix of adenosylcobalamin and methylcobalamin, which you absorb under your tongue. About £25 a bottle and lasts a couple of months. These are the most bio-available forms, one which works in the brain and one in the mitochondria for energy.
Then a general all the B vitamins tablet, & check for getting enough potassium.
I take the above first thing every morning, on an empty stomach.
In the evening (& at least 2 hours after caffeine and food), I take iron (ferrous fumarate or iron bisglycinate generally better absorbed and tolerated) with vitamin C (orange juice etc also fine, doesn't have to be a supplement). Some evidence showing iron is better absorbed if you take it every other day, so I do 200% RDA alternating days.
Magnesium at bedtime can be helpful as well.
But, I don't have coeliac, so go back and check in with your doctor / do your own research.
I haven't done it, but private clinics will do B12 injections for about £30-40 per dose, and iron infusions for about £300 per infusion, but they will want blood tests to check that that is appropriate treatment, although they'll be working to better ranges than the NHS ones. I don't know if they accept NHS blood tests or would charge more to do their own.