I am currently on a high dose of thyroxine (250mcg). I do not have any symptoms of hyperthyroidism. Should I be concerned by this high dose?

Depends on your TSH. Some patients require higher doses of medications. Your physician should monitoring your thyroid function via blood tests (tsh). Typically, a TSH is checked 6-8 weeks after starting a new dose and at least once a year once your dose is stable. If you have a lot of weight loss or gain you may need rechecked as well. If your TSH is in a good range then you need that high of a dose.
Follow your TSH . Replacement of thyroid hormone in patients with hypothyroidism is usually monitored by checking labwork -- TSH and free T4 levels. Usual intervals for checking would be about every three months. If it's been a while since you've had yours checked, you should see a doctor to discuss this. The actual dose is not important, the goal is to have your labwork in the right range.