[SalesForce] Database.convertLead() creates Account, Contact and Opportunity but leaves Web-to-Lead Lead unconverted

I've written a trigger to auto convert leads coming in from a web form. When I send the information from the web form, the Lead is created, the trigger runs the Database.convertLead and I get an Account, Contact and Opportunity. However looking at the Lead tab I see the Lead I just entered, it was not converted, or at least it was not updated as IsConverted.

Trigger:

Trigger AllLeadTrigger on Lead (after insert)
{

    List<Lead> autoConvertLeadList = new List<Lead>();
    for (Lead l : Trigger.New)
    {
        if (l.LeadSource == 'Partner Webform' || l.LeadSource == 'Employer Webform')
        {
            autoConvertLeadList.add(l);
        }
    }
    if (!autoConvertLeadList.isEmpty())
    {
        AllLeadTriggerHelper.ConvertLeads(autoConvertLeadList);
    }

}

Class:

public class AllLeadTriggerHelper
{

    public static void ConvertLeads (List<Lead> leadList)
    {
        if (leadList.isEmpty())
        {
            return;
        }


        LeadStatus convertStatus = [SELECT Id, MasterLabel FROM LeadStatus WHERE IsConverted=True LIMIT 1];




        List<Database.LeadConvert> lcList = new List<Database.LeadConvert>();
        for (Lead l : leadList)
        {
            if (l.IsConverted)
            {
                continue;
            }

            Database.LeadConvert lc = new Database.LeadConvert();

            lc.setLeadId(l.Id);

            String opName = l.Company==null?'':l.Company
                            + ' - '
                            + l.FirstName==null?'':l.FirstName
                            + ' '
                            + l.LastName==null?'':l.LastName;
            opName = opName.left(120).trim();
            lc.setOpportunityName(opName);

            lc.setConvertedStatus(convertStatus.MasterLabel);

            lcList.add(lc);
        }


        List<Database.LeadConvertResult> lcrList;
        if ( ! lcList.isEmpty())
        {
            lcrList = Database.convertLead(lcList, False);
        }
        for (Database.LeadConvertResult lcr : lcrList)
        {
            System.Debug('@@@@@@@@'+lcr);
        }

    }


}

When I check the debug log I see the leadConvert was a success, records are created but the Lead is not closed/converted.

21:45:08.004 (1004171117)|USER_DEBUG|[52]|DEBUG|@@@@@@@@Database.LeadConvertResult[getAccountId=001m0000009zLtNAAU;getContactId=003m0000007zEppAAE;getErrors=();getLeadId=00Qm00000026BDyEAM;getOpportunityId=006m0000002gMjlAAE;isSuccess=true;]

When I run this Query

SELECT Company, ConvertedAccountId, ConvertedContactId, ConvertedDate, 
       ConvertedOpportunityId, FirstName, IsConverted, LastName 
FROM Lead

I just see blanks in the 'converted' fields for the Lead.

If I key in a Lead in the Salesforce screen, and set the LeadSource to one of the values the trigger expects then it auto converts exactly as I would expect. This just seems to happpen to web-to-lead Leads.

[I have tried deactivating all workflows and also changing the class/trigger api from 32 to 28 but it made no difference]