No, the costs are extra. Indeed if you look at the claim form there are boxes at the bottom for
Amount of Claim
Court issue fee
Solicitors costs
The costs in SCC are fixed. When you do the claim form you include a "pleading" in the claim for costs - eg
AND THE CLAIMANT claims
1) damages for breach of contract
2) interest pursuant to s69 County Courts Act 1984
3) costs
If you are successful to recovering the claim, you are then entitled to the fixed costs - issue fee, allocation fee, hearing fee and solicitor's fee. You may also get further costs if the other side have acted unreasonably.