Ethical web designers should offer their contact details. Ensure that your designers provide their full name, address and contact numbers and confirm this before doing business with them. If you don't you may find that you are dealing with someone who is working as a web designer on the side and unlikely to be around for lomg.
Ethical Web Designers here in the UK have no reason to hide their contact details from
you.
However many "fly by night" people pass themselves off as proper web designers in an attempt to make a quick killing without paying any UK tax.
Clearly it is not in these "web designers" best interests to offer you (or the taxman) their full contact details.
They can often provide a reasonable web design job but you can be certain that problems will arise as a result of your dealing with them.
If you are considering a web design company that is not willing to tell you who or where they are then beware. Ask yourself why they want to keep this information hidden.
Typically these web designers will offer only an online form as a means of contacting them.
They will not offer an email address or full contact details and generally they will only provide a mobile phone number.
Designers like these are to be avoided if you are serious about your business's website.