This could lead to a fast-track passage of the much delayed private Lloyds TSB Bill.
Further disruption may come, however, in the shape of the Hill Samuel Action Group, which has recently formed to fight for a better pension deal from the TSB, which owned the now defunct merchant bank.
On Thursday, Banking, Insurance and Finance Union (Bifu) assistant secretary John Townsend held talks with Lloyds TSB over the petition the union has submitted against the Bill.
Bifu wants the Bill redrafted to incorporate four demands by the union. The internal Lloyds TSB Union has also petitioned against the Bill. Bifu's demands are: no compulsory redundancies; customers, staff and local communities to be consulted before any branches are closed; harmonisation of terms and conditions of staff at Lloyds and TSB; and full union recognition.
Mr Townsend said that the two sides were close to an agreement, and he would expect to be able to ballot members on the management's latest proposals within a month.
If the members agree to Lloyds TSB's conditions, Bifu will drop its petition against the Bill.
Until the Bill is enacted, Lloyds TSB will find it difficult to proceed with any branch closures, thereby justifying the logic of the merger to investors. At the time, Lloyds TSB promised the merger would deliver savings of pounds 350m.
The Bill had its second reading in March, when several Labour peers voiced concerns about the merger.
On the Tory benches, Lord Cobbold, the former treasurer of Hill Samuel, also raised concerns about the status of the TSB pension scheme.
The Hill Samuel Action Group is concerned about a surplus in the Hill Samuel pension scheme, which is worth pounds 200m. TSB's scheme, into which the HS scheme was subsumed, is now overfunded by pounds 1.3 bn. The surplus is being eliminated by a long- standing contributions holiday. However, former pensioners at Hill Samuel believe some of the surplus should be transferred to members, current pensioners, and early leavers - those made redundant when HS closed.
HSAG has been founded by former employees of the bank. Membership of the group numbers more than 500. A formal circular is expected to be released to HS pensioners in the next week, which will detail its demands and advise pensioners on action they can take.