First of all it is worth stating that UK law does not officially recognise the code for a website as being a literary work for copyright purposes. The law does recognise computer programs, but as far as I am aware the courts have not ruled on whether the code for a browser to construct a website on a viewer's screen constitutes a computer program or not. Clearly there are parallels and some differences. The remainder of my response is based on the premise that your source code does have the same protection as a computer program.
So given that, you are right that in the absence of any formal agreement between you and your client, you own the copyright in the websites you develop. And also you are right that when a client commissions and pays you to develop a website for them, it is implicit that they will be able to use your work without any further constraints. But as you have highlighted, exactly what they can do in terms of further exploiting the site is not at all clear. This is where in future you should consider having a standard agreement available for commissions. Theoretically unless the client has mentioned future development at the commissioning stage, all he is entitled to from you is use of the site you created. It does not entitle him to find someone else to modify (see below) your copyright work. However in the real world things aren't really so straightforward. As you are well aware no-one actually needs to come to you to your source code because by definition it is available to download and copy by anyone. Even the more esoteric bits, such as Flash, can be de-complied relatively easily so really all your intellectual property is out in the open and you have a hard job to protect it. Personally I would suggest the approach you should take is to price for a one-off job and then agree a separate fee for maintenance and further development work (possibly on an hourly basis), so that if at any stage the client does take his business elsewhere, you can let go of your work (even though still owning the copyright) without too many qualms.
The difficulty you face is somewhat like a portrait painter. You do the work and own the copyright, but the client gets to keep the work and can hang it in their toilet (=put in on the www), sell it or even destroy it and you have no say in the matter. Most websites will have a very short shelf life before they either need updating or completely replacing. This is as much to with technical changes (browser features, IPv4, HTML5 etc) as it is to do with the actual content. And of course the client may well be providing much of the actual site content - images, product details, databases, etc to slot into your structure. This makes deciding a time limit for the implied licence very difficult. And it may also be implicit in the licence that it is exclusive to the client. If you design site for the Acme Vacuum Cleaner Co, you would be constrained from selling the exact same site (with different wording) to the Whizzo Vacuum Cleaner Company.
As you will have noted, I haven't really answered your questions because there are two answers in each case: the 'legal' one and the real world one. I don't suggest that a court would find it any easier to give straight answers either, because obviously a court would only become involved after the event when the facts of the case were known, whereas you are (hopefully) asking hypothetically.
Remembering my first point about your code and computer programs, one final point worth bearing in mind is that several special rules apply to computer programs:
Section 21 of the Copyright Designs and Patents Act 1988 says that adaption is not permitted. Adaptation
"in relation to a computer program, means an arrangement or altered version of the program or a translation of it; ...
(4) In relation to a computer program a “translation” includes a version of the program in which it is converted into or out of a computer language or code or into a different computer language or code"
However, the Copyright (Computer Programme) Regulations 1992 permit computer programs to be de-compiled in certain specific circumstances in order that other programs may be made compatible with them. This is only permissable when there is no other means of obtaining the relevant data. So with your code it might be seen as lawfull to develop the website by adding additional code to yours in order to extend the functionality (say by adding a shopping cart feature) which would obviously need to hook into you code at various points. Furthermore Section 50C of the Copyright Designs and Patents Act 1988 (as amended) says:
"50C. Other acts permitted to lawful users.
— (1) It is not an infringement of copyright for a lawful user of a copy of a computer program to copy or adapt it, provided that the copying or adapting—
(a) is necessary for his lawful use; and
(b) is not prohibited under any term or condition of an agreement regulating the circumstances in which his use is lawful."
I have to honest and say I have no idea whether that provision could be applied in the case you mention, but it gives an indication of how the courts might
view the respective rights of you and your client in the event of a dispute over a site you designed.
If this is more than a hypothetical inquiry, I strongly urge you to speak to a good IP lawyer for more detailed advice. But what ever it is, I suggest you look into the idea of having a standard agreement (such as this:http://www.own-it.org/contracts/22
) for all future business.