I have recently had a couple of queries regarding these conditions and whether or not someone with them would qualify for DLA - both child and adult. Previous experience has been that the claimant had other conditions in addition to these, eg, learning difficulties or speech and communication delay. Does anyone have any experience of a claimant getting an award of DLA who purely has dyslexia and/or dyspraxia and nothing else?

Not at all easy - As with most medical conditions, whether or not the these conditions would assist the Client getting an award of DLA will depend upon the severity of the condition.
Google up the conditions and read up about them - try the Dyslexia and Dyspraxia support websites - then talk to the clients about how the conditions affect them on a day to day basis - with Dyslexia you are primarily looking at communkication difficulties -

with dyspraxia you are dealing with the failure of coordination between the brain-eyes-hands and feet - the proverbial clumsy child.......

We have had quite a lot of success with these types of conditions (at appeal anyway!) with both adults and children. However some of the care needs are extremely subtle and do not lend themselves to the postal DLA process. Moreover, parents may not even recognise some of the effects.

The DANDA site is good for info: http://www.danda.org.uk/ and their chart is very useful for helping parents identify issues:http://www.danda.org.uk/pages/neuro-diversity.php (click on it and save as a PDF file).

Another site with good info (esp. for adults) is the Civil Service:

http://www.civilservice.gov.uk/people/diversity/toolkits/dyspraxia.aspx

Nearly all the people I have seen have overlapping symptons which can/may give rise to care and/or mobility needs. Having said that, everything is a matter of degree, so simply having a diagnosis is not enough. Many needs will only become apparent when children reach their teens or early 20s, esp. when they move out of the family home and cannot organise themselves. With young adults living alone we have sometimes referred them for Supporting People floating support services.