In the US & UK on more than $6000 & GBP 3000 bank has to notify law enforcement agencies. Ehtasab, you can transfer millions, just have to go through security check/clearance.
Kash speak to your Bank, i ran into a delayed money transfer, when i did it for the first time, amount was little over GBP 6000. it took 3 weeks, now it takes 2-4 business days.
Banks notifiying law enforcement is different than "limit the transfer". The max you can transfer without appearing in LEA radar is $10,000 in US, don't know about UK.