In Golden Ocean Group v Salgaocar Mining Industries the Court of Appeal has confirmed that a guarantee can be constituted by an exchange of e-mails.
See this useful note by Fenwick Elliott (at pages 8 and 9), which also discusses more generally how contracts can be formed by e-mail – and that as, in this case, the sender’s Christian name at the end of an e-mail will be all that is required for a signature.