The modem power lead looks to be about 2 metres. I'm not disconnecting mine to get it accurate.
(Strictly speaking, it isn't an Infinity modem, it is an Openreach VDSL2 modem which is supplied on all FTTC connections by any ISP. Infinity is just the BT Retail product using FTTC. See
this page for a list of several other ISPs, and the spreadsheet link on there for summary details).
It can be run off an extension lead anyway - mine is.
The Home Hub, (which is an Infinity only product), power cable I have no idea about, but again 2 Metres seems to be the norm. It too can be run off a mains extension lead, and the ethernet connection between the modem and Home Hub can be up to 100 metres. Though I wouldn't like to rely on that! The supplied ethernet cable I expect is 1-2 metres.
The installing engineer can site the modem up to 30 metres from the master socket anyway, using the
Data Extension Cable that most ISPs specify when ordering on your behalf. Friendly engineers will even resite your master socket.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost.
Internet connection - Plusnet Value Fibre.
"Where talent is a dwarf, self-esteem is a giant." - Jean-Antoine Petit-Senn.