First I looked up the author, Mary Gentle, who was born in Eastbourne on the south coast of England. Eastbourne itself was then my first guess, but it didn't seem to fit: there's no castle in the town (the closest one being Pevensey a few miles away), and to the west of the town lies the massive Beachy Head, rather than a "West Hill" which divides the "Old Town" from the modern portion.
Not to be put off, however, I started widening my net. Assuming that the towns Mary Gentle is most familiar with would be somewhere reasonably close to Eastbourne, I checked a list of towns in East Sussex. Since we want a town that's fairly large but also fairly isolated, not surrounded by suburbs and smaller towns like Brighton, my next guess was Hastings. The Wikipedia article for this town (emphasis mine) was already enough to make me strongly suspect it's the one we're looking for:
Hastings is situated where the sandstone beds, at the heart of the Weald, known geologically as the Hastings Sands, meet the English Channel, forming tall cliffs to the east of the town. Hastings Old Town is in a sheltered valley between the East Hill and West Hill (on which the remains of the Castle stand). In Victorian times and later the town has spread westwards and northwards, and now forms a single urban centre with the more suburban area of St Leonards-on-Sea to the west.
Compare this with the description of Surcombe in A Hawk in Silver: Holly is on the East Hill and extending her gaze westwards to see first the Old Town, then the West Hill and the Castle, then the modern town which has spread out westwards, then another small town, then a long sweep of land ending twenty miles away at a chalk headland.
The next town to the west of Hastings is Bexhill (corresponding to "Combe Marish" in the story). Between Bexhill and Hastings is a stretch of low-lying land, Glyne Gap, which is now home to a retail park but could well have been marshland decades ago. The next large town is Eastbourne, which probably corresponds to "Deepdean", and certainly the "Chalkspit" jutting out into the channel must describe Beachy Head.
The description of East Hill, from immediately before the passage quoted in the question, also fits exactly:
Jesus, today's hot! Coming to the end of South Street, she looked undecidedly down the main road to the overcrowded beach. Not a hope. I gotta get out of here for a bit.
She threaded her way quickly through the crowds to the Fishmarket. A few minutes later she was at the top of Tackleway Steps, at the foot of the East Hill.
Where it faces the sea this is a sandstone cliff pocked with caves. On the town side a steep gorse and bramble-covered slope has one twisting stairway leading up it. At the summit a grey rock juts out like a ship's prow. Beyond that lies high, wide and grassy downland, the gorse-yellow Fire Hills and Starshell Cove.
There is a South Street in Hastings, which meets the "main road" (London Road) close to the beach. The East Hill is a sandstone cliff, looking sheer from the sea side but with a path up behind it. Beyond it to the east is a wide sweep of downland and a bay with a naturist beach.
Here are images of the East Hill at Hastings, and of the Old Town from the East Hill. (Click for full-size versions.) The second picture is much like what Holly would have been seeing in the passage quoted in the question. Note how the main road really does wind like a dragon through the town!
Most clinching of all, the road just on the town side of the East Hill is indeed called Tackleway. This seems to be the only distinctive name which isn't altered in the novel - perhaps as a sort of Easter egg, a nudge and a wink to people familiar with Hastings.
Let's check everything on a map (the red indicated point near the right-hand side is Tackleway):
It's virtually 100% certain that the town being portrayed by Gentle's "Surcombe" is Hastings. A fitting place, perhaps, for an invasion from the sea to take place!