In a similar boat something to consider is the break free will change daily with market rates but also the reference rate had probably moved to 1 years rate rather then 2 year rate so might be worth checking break free again (on my list of things to do).
On the logistics the whole process is a lot less drawn out when compared to purchasing a place as it's only between two parties (you and loan provider) and doesn't include a seller.
Loan approval should last for 6 months. So something that you could start mid year if targeting September. Again given potentially small break free you might consider going earlier. Really need to compare break free versus higher interest charge to know what's best.
From loan application to approval you're probably talking weeks. Though I did see a post on here discussing delays... But not sure how representative that issue was.
Legal aspect of things.. assuming you're using the same solicitor that should have all the paperwork so shouldn't add too much to the process. That's assuming your home has no unusual characteristics that might raise concerns.