This is known as Funds at Lloyd's. The level of Funds at Lloyd's determines the amount of insurance business a member can underwrite.
The amount of funds required from members will vary, depending on the perceived level of risk in the business which they underwrite. This is known as "Economic Capital Assessment" or ECA.
More information about funds at Lloyd's.
Funds in syndicate (FIS)
Members' capital to support underwriting has traditionally been held as funds at Lloyd's (FAL), however, it can now also be held by aligned corporate members within their syndicate's premiums trust fund (PTF). The most recent Market Bulletin on the subject was Y4032, dated 29 June 2007 entitled "Capital advantages: Aligned member capital held in syndicate PTFs".
More information about funds in syndicate