Welcome! In the world of extension leads there are various levels of quality and construction. The extension lead needs to be rated for 13A (some are rated lower!). The socket should be weatherproof if it’s left outside for any period of time as well.
Always check the plug on the Twizy and the plug inside the garage whilst the twizy is charging, to make sure the plug is not getting hot. Some cheap sockets and plugs tend to get too hot after a few hours pulling a continious load, so it is worth being wary of.
Lastly - I would personally avoid plug top timers as whilst some claim to handle 13A, many are poorly constructed and might not be able to take the 2kW the twizy pulls for 3+ hours for a full charge.
In the long term, it’s better to arrange for a proper Masterseal 13A weatherproof outside socket to be installed where you intend to charge up.