The writs will follow the dispatch of warning letters earlier this week to all UK names and some from overseas who refused to sign the pounds 3.2bn rescue plan agreed last month.
They have been told to pay up within days or be prepared to argue their cases in court.
Lloyd's has left the door ajar for names who change their minds as a result of the threat of legal action, who may be allowed to join the rescue plan late - but the final decision on each case will be made by the market's ruling council.
"The council will be entirely pragmatic," a Lloyd's spokesman said.
Lloyd's said that 119 late acceptances had been agreed by the council, many of them because the settlement papers did not reach the names until close to the deadline last month.
Those who sign up for the reconstruction programme gain a substantial reduction in the debt they owe the market.
The 900 warning letters sent out this week covered roughly pounds 250m of the pounds 500m debt remaining to be collected.
They included all the overseas names, other than those living in the US. Legal actions against American names are proving more complex to get off the ground because of variations in creditor laws between individual states.
Altogether, just over 1,800 of Lloyd's 34,000 members have dug their heels in and refused to sign up for the reconstruction programme, which has now gone through.
Lloyd's debt collectors are not planning to take all 200 names hit by writs to court immediately. A spokesman said the writs were to be enforced on a "selective basis".
The first batch of warning letters from the solicitors Dibb Lupton Alsop told names that unless they paid "within days" proceedings would be commenced to cover the full sums outstanding together with interest and legal costs.
In court, Lloyd's plans to cite two previous judgements in its favour. Lloyd's, under chairman David Rowland, believes it has a right under its agreements with names to demand payment immediately, ahead of any litigation over the rights and wrongs of a case.
This was upheld in the Higgins case and confirmed on appeal.
Lloyd's is also relying on a court judgement that backed its right to pay names' debts from its central fund and then collect the money later from the names. This was upheld in the Clemenson case.
Rebel names have been expected to contest this decision but no appeal has yet materialised.
The refuseniks have formed a new grouping, the United Names Organisation, which plans to fight Lloyd's in court, using allegations of fraud in the market to justify their refusal to pay.Reuse content