How long from local searches to completion?

We bought a house 5 weeks ago, survey and mortgage offer are in place with no problems arising from either of these. The local searches should be returned to me solicitor within the next 2 working days, how long from these being returned to completion?

no chain on either sides and both want to move asap, but their solicitor seems slow at responding to enquiries (3 weeks and no reply to initial contract enquiries - but seller is chasing this up monday)

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