Just on when people should declare a disability...
It's not 'lying' to say on an application form that you don't have a disability and then declare it when offered the job.
It is up to the individual if/when they declare a disability and the only reason to really is if you will require some adjustments under the Equality Act 2010.
LolaSmiles re: your hypothetical situation. Ideally, the person should disclose their disability early on so that adjustments can be put in place to avoid performance issues arising. However, even if someone doesn't and declares their disability during a performance management process, the employer is still obliged to make reasonable adjustments. Not making them would be discriminatory, as would judging someone performance without taking into account their disability once they'd disclosed it.
Performance management is actually the most common time for people to disclose a disability. It's is fear of discrimination that prevents people declaring it beforehand.
WatchingTheRaindrops I disagree that individuals choosing not to declare their disability is what perpetuates discrimination. It's stunningly naive to think that disability discrimination is a thing of the past, I'm afraid.
I would agree with OP's career advice - get further along the recruitment process before declaring anything. It's easy for organisations to just not offer someone an interview if they declare a disability on their application form, much harder to withdraw a job offer if someone declares a disability when they're appointed.
Having said that, being dyslexic can be a positive in education - you'd be an excellent role model in terms of what can be achieved and how the law can support people.
Best of luck OP.