RecA binds/protects ssDNA and enables intercalation into the dsDNA. The mechanism of HR in E. coli is not 100% resolved and might work simply via incorporation of the ssDNA into the newly synthesized dsDNA during replication. This claim is supported by higher recombination efficiencies when using ssDNA complementary to the lagging strand.
See "Lambda Red Recombineering in Escherichia coli Occurs Through a Fully
Single-Stranded Intermediate" by Mosberg et al (2010) for further information about the mechanism presumably utilized in Lambda Red recombineering.