For the proper functioning of government and to avoid executive abuse of power, MPs should have constitutional immunity from arrest. The police must make an application to the speaker who would pass it on to a committee which would based on the evidence presented allow or disallow arrest.
An MP may be prosecuted in absentia. Either way he would be free to attend his trial and defend himself while free and attending to his duties.
It is very simple to understand why certain countries took that step: A President can lock up enough MPs and keep them away from parliament to ensure he has a majority to pass certain laws. Fortunately, constitutional amendments require a QUORUM without which any business becomes a nullity.