+1 to what AlexanderC said about not mentioning it on your CV or in the early interviews. Really, it's nobody's business and even though the law says that employers can't discriminate against us, employers
can and
do use any reason they like to discriminate against people they don't want. But if you are going to transition on the job, your safest bet is to wait until after you have a written job offer and then tell the Personnel Department or your line manager that you're trans and may need time off for the occasional medical appointment. They will need to know this (and about your deafness) if you want to enjoy the protections offered by UK law.
My GIC seemed to think that all their patients are entitled to paid time off for appointments related to their transition. I'm not 100% sure that this is enforceable but there's a good chance that it would stand up in court. You see, gender reassignment is a Protected Characteristic under the Equality Act 2010, so they won't be allowed to refuse you time off for such appointments and you shouldn't suffer any detriment because of them (such as loss of pay or holiday). However, if there is a dispute you might have to take them to a Tribunal to assert your rights.
According to the Equality Act, your employer has to treat time off for medical appointments due to disability or gender reassignment in exactly the same way as they would treat time off for doctors' appointments attended by any of your colleagues for any reason. But since we have no universal entitlement to paid time off for such appointments, each company makes their own policies for such things. So the worst-case scenario is that if it's a rule that all staff have to 'clock out' for doctors' appointments or make up the time, chances are that your company will try to make you do the same.
If the company generally pays staff for time they take off for doctors' appointments, they'll have to pay you too. As long as the reason is related to gender reassignment or disability, you're covered by the Equality Act so they have to treat you the same as any colleague going for a routine medical appointment or operation. So my top tip would be to find out what their policy is for doctors' appointments, hospital stays etc. before you tell them you're trans.
When I came out to my boss one of the first questions he asked was whether he'd have to pay me for time off for any medical appointments related to my transition; he was rather hoping I'd use up my holiday. So I said that according to my GIC I'm entitled to paid time off for any medical appointments related to my transition... but I reassured him by pointing out that (as you rightly say) there are generally a couple of months between appointments, and it's likely to be at least a year until I qualify for the first surgery, so this is a slow process with lots of gaps in between. He was worried that I'd be off work most of the time; he just needed reassurance that that wouldn't be the case.
Your deafness is a disability so it's also protected by the Equality Act. Again, you're entitled to time off for that in accordance with your company's policies on time off for medical appointments. I know this because I had a profoundly deaf colleague who took time off every week or so for his deafness-related appointments (speech therapy, etc.) - and the company had to pay him for that too.
Any time off for asthma would be treated the same as for any other doctor's appointment.
Here's the Equality Act in full:
http://www.pfc.org.uk/pdf/Equality_Act_2010.pdf - it's worth read. Once you've downloaded it, search for the word 'gender' to see the protections to which you're entitled. Also look at the protections you get due to disability.
Oh, and my GIC is so far away from work that it would be a 7-hour round trip from the office... so my employers have to pay me for a whole day off work so that I can attend my appointments.
