It sounds like your doctor knows what he is doing. You are clearly under-replaced. Hopefully with this increase you will start feeling better in a few weeks. You may want to increase more slowly though. Perhaps up to 100mcg for 4-6 weeks then to 125mcg.
Ideally, on levothyroxine (I'm presuming that is what you are taking), you can expect your TSH to get to below 1 before you feel better. Some people are fine with it a little higher but most need it to be lower. TSH (the test you had) increases when your thyroid is underactive and decreases when you get to a high enough dose of thyroxine.
If you find that you still don't feel well once on a dose that reduces your TSH to below 1, it might be a good idea to get the following tests;
ferritin (stored iron)
These are very common deficiencies in people with hypothyroidism and can prevent us from feeling well even when on the correct dose of thyroxine. Don't just accept the NHS ranges for these. Please post them on here so we can advise whether you may benefit from supplements.
I hope you feel an improvement soon