For stocks and shares ISAs, industry guidelines recommend that the full transfer process takes 30 days from start to finish (from receipt of your application). However, you need to be aware that this can depend upon the availability of proceeds from the sale of your stocks and shares ISA.
Stocks and shares ISAs can include a variety of investment-types which could each take different times to close down or sell, this may mean that it takes longer than 30 days for your current manager to make the proceeds available for transfer.
In transferring in a stocks and shares Junior ISA or a Equity Child Trust Fund (stocks and shares), the industry recommendation is that the process takes 30 days. However, this will depend upon the time taken by your managers to sell the funds that you have invested in.