Gilbert has been in the job since January after Lloyds TSB acquired HBOS.
He is responsible for brands including Lloyds TSB, Cheltenham & Gloucester, Halifax and Bank of Scotland.
He joined Lloyds TSB in October 2006 from Lowe Group Asia-Pacific as group marketing director before taking on the broader role in January.
Gilbert was responsible for the development of Lloyds TSB’s “For the journey…” proposition and was also the architect of Lloyds’s sponsorship of the London 2012 Olympic and Paralympic Games.
The bank says it has started its search for a replacement. It is understood Gilbert does not have another job to go to.
The banking group, 43% owned by the taxpayer, recently appointed Mediaedge:CIA to handle its media planning and buying.
It recently announced the new structure of its marketing team, which included the appointment of former Visa marketer Joe Clift as head of brand/customer marketing specialist brands.
Gilbert also had stints at Young & Rubicam, as executive vice-president as well as at Collett Dickenson Pearce as a director.