The Financial Conduct Authority (FCA) said a review into the way claims on these types of policies are handled has shown that around two-thirds of claimants were happy with how they had been dealt with.
It said that any delays to customers' claims being processed are likely to be down to poor processes or management, as the FCA found no deliberate attempts by firms to drag their heels.
Some 65% of household insurance customers were satisfied with the way their claim had been handled, as were 64% of travel insurance claimants, the FCA said.
The regulator said it has "uncovered no evidence of systematic attempts by firms to deny valid claims or to squeeze settlement costs".
The FCA launched the review last Spring and is finalising its findings before publishing a full report in May.
It said while these findings were "broadly positive", firms should look again at the way that medical conditions are treated in travel insurance policies, how they keep in touch with customers while claims are progressed and how incoming calls are recorded and used.