Actually the law was written very carefully so as not to be tied just to cookies. Regulation 6 of the Privacy and Electronic Communications Regulations 2003 (PECR) [1], after applying the 2011 amendment [2] reads:

    (1) Subject to paragraph (4), a person shall not store or gain access to 
        information stored, in the terminal equipment of a subscriber or user
        unless the requirements of paragraph (2) are met.
    
    (2) The requirements are that the subscriber or user of that terminal 
        equipment-

        (a) is provided with clear and comprehensive information about the 
            purposes of the storage of, or access to, that information; and
            
        (b) has given his or her consent.

    (3) Where an electronic communications network is used by the same person to 
        store or access information in the terminal equipment of a subscriber or
        user on more than one occasion, it is sufficient for the purposes of
        this regulation that the requirements of paragraph (2) are met in
        respect of the initial use.

    (3A) For the purposes of paragraph (2), consent may be signified by a 
         subscriber who amends or sets controls on the internet browser which 
         the subscriber uses or by using another application or programme to 
         signify consent.

    (4) Paragraph (1) shall not apply to the technical storage of, or access to, 
        information—

        (a) for the sole purpose of carrying out the transmission of a
            communication over an electronic communications network; or

        (b) where such storage or access is strictly necessary for the provision 
            of an information society service requested by the subscriber or user.

No mention of cookies, and "information stored, in the terminal equipment of a subscriber or user" would seem to apply to solutions that use HTML5 local storage, ETag headers, Flash LocalSharedObjects or any other similar technologies.

[1]: http://www.legislation.gov.uk/uksi/2003/2426/contents/made

[2]: http://www.legislation.gov.uk/uksi/2011/1208/contents/made

Because obeying the (spirit of) the law is so incredibly onerous?