Yes. All dogs are eligible as long as they a) are not aggressive to humans or other dogs b) They are not ill or heavily pregnant c) not banned breeds in the UK 
I live in and cover Bromsgrove, Worcestershire. In particular, the B60 and B61 post codes, but may be willing to cover elsewhere if possible.  
I do have transport to get to customers. 
Currently, I am operating 5 days a week (weekends available if booked at least a week in advance. There is NO EXTRA CHARGE for weekends, however bank holidays are charged at £2 extra per dog). I am happy to take the dog(s) on walks in any weather condition EXCEPT FOR IF IT IS TOO HOT. I can not stress enough how dangerous it can be to excercise a dog in extreme heat, and will not walk in 20°C or more. If it is too hot, a stay and play will be offered if available, or a trip to undercover woods if suitable. 
If I am unable to operate due to this, or illness/other unforeseen circumstances, I will endeavour to let the client know as soon as possible. Any sessions already paid for will either be refunded or rolled over, whichever suits the client. 
I have undertaken training in pet CPR and basic animal first aid. If the incident is serious enough, I will apply any of the skills needed in order to help your dog as much as possible. It may be necessary to transport your dog to the nearest vet who will have been notified. At this point, you the owner will be notified. This will ONLY be done after a consent form is signed at the initial consultation...
Any new customer registering their interest in the service will have a brief consultation before hand. This will usually only take 5 - 10 minutes and is just to get some basic information about your dog (existing medications, behaviour habits etc).
A consent form will have to be signed to grant permission to take a severely ill dog to the nearest vet.
I will only have 5 dogs at any one time. It allows me to offer a better, personalised service to each dog in my care at the current time.

Yes, I have been fully DBS (formerly CRB) criminal checked and am happy to provide proof if necessary.