* BoE rejects primary competition remit
* Woods says stuck with "local fixes" for EU rules (Adds more details)
LONDON, Feb 27 (Reuters) - The Bank of England will not "go soft" on enforcing European Union capital rules for insurers, but will look at ways to make it easier for new entrants to boost competition in the industry, its deputy governor Sam Woods said on Tuesday.
The BoE's Prudential Regulation Authority (PRA), which Woods also heads, is consulting on how to ease the burden of the EU's Solvency II rules, which insurers say are overly burdensome.
It follows a hard-hitting report from British lawmakers in October which accused the PRA of focusing heavily on how much capital insurers hold rather than whether they can compete globally.
Woods said he was not living in an "ivory tower" and was willing to make some changes, but would not be rushed into making any big alterations.
"We can tell the difference between feedback about a genuine technical flaw and generalised lobbying for lighter-touch regulation," Woods told the annual conference of the Association of British Insurers (ABI).
And the industry should not lose sight of the policyholder, who has been saddled with past failures like Equitable Life.
There is "no convincing evidence" to show that the EU rules had crushed profitability or growth of British insurers, or driven up premiums for policyholders, Woods said, although implementation of the directive could work better.
Parliament's Treasury Select Committee wants competition to be a primary objective of the PRA alongside the safety and soundness of insurers. Some business is already going overseas because of how the PRA applies EU rules, it said.
"The point of that debate is not the PRA having a competition objective, but it's about competitiveness of the UK on the global stage," ABI Chair Andy Briggs said.
But Woods rejected the Treasury committee's call, saying it could detract from the PRA's current main aim of ensuring safety and soundness.
"I am not therefore persuaded of the case for giving a primary competition objective to the PRA," Woods said.
EU regulators have declined to make some of the changes that lawmakers want, leaving Woods with what he called "second best" local fixes.
He was emphasising how the PRA could change the way it enforces some of the Solvency II rules, rather than changing the rules themselves, a step that could trigger opposition from other regulators in the bloc.
Britain is leaving the EU next year, with trading terms uncertain for financial firms who may have to rely on a system of "equivalence" for access to the bloc's market.
Actually changing the substance of EU rules could make it harder for Britain to argue equivalence, an insurance regulator from elsewhere in the EU told Reuters.
(Reporting by Huw Jones; Editing by Alexander Smith and Susan Fenton)