As with most problems that occur on lawns preventative is better than cure. Try not to let the lawn dry out too much during periods of drought. If it does become a problem the infected areas can be spiked to try and get the water down into the soil profile.
To treat the hydrophobic area a wetting agent can be used, which is type of detergent. Wetting agents are widely used in the golf and sports turf industry to combat dry patch problems. Wetting agents help reduce surface run off and help the water move through the root zone to where it is most needed.
Any aeration before applying a wetting agent would be very beneficial and increase the effectiveness of the wetting agent.
Dry patch would only be a severe problem during very dry summers, on lawns with a light sandy soil. It should not be problem during a normal wet British summer.