Naturally we can accept undertakings from solicitors. The Law Society has also made it clear in the Conveyancing Handbook that we can "normally" (that is to say, unless you know of a good reason why not and subject to the adequacy of that firm's insurance) accept an undertaking from a licensed conveyancer or a firm of licensed conveyancers. The Council for Licensed Conveyancers operates like the SRA and can discipline those who default on an undertaking. The courts cannot enforce an undertaking given by a licensed conveyancer. This is different from an undertaking given by a solicitor. Bear in mind that small firms and licensed conveyancers might have modest insurance. The minimum is £2m. When dealing with undertakings for sums bigger than this, you will need to discuss the matter with the client. Best practice is to require the other side to use a better insured firm. This should be unlikely as it is not in the interests of a firm to take on work with a value higher than their PI cover, but that is not to say it does not happen.
You cannot accept an undertaking from an unregulated firm (which should not be doing conveyancing anyway) or a member of a licensed firm who is not a director/partner of the firm or themselves a solicitor.