The only way to be absolutely sure is to ask the airline.
As the ticket was issued by an agent, the airline would usually be unwilling (or contractually unable in many cases) to amend the ticket, but they can advise you as to the restrictions placed on the ticket, including whether you have to complete all legs of the ticket in order.
If you want to do the legwork yourself, you can always check the airlines conditions of carriage.
Coupon Sequence and Use
3.3.1. If you have chosen a tariff which provides for you keeping to a strict ticket sequence,
please note the following: If carriage on a previous leg of the journey is not used or not used in
the sequence anticipated on the ticket, the fare charged for that flight will be the fare that
would have applied to your differing but actual route at the point of booking. If this fare is
higher than the fare for the route indicated on your ticket, we can make further carriage
conditional on you subsequently paying the additional charge which has accrued.
So I read that as there is no automatic cancellation of the later legs on the ticket, but there may be a charge made.
However, British Airways states:
3c2) Your ticket is no longer valid if you do not use all the coupons in the sequence provided in the ticket. Where you change your travel without our agreement and the price for the resulting transportation you intend to undertake is greater than the price originally paid, you will be requested to pay the difference in price. Failure to pay the price applicable to your revised transportation will result in refusal of carriage.
Which indicates to me that they reserve the right to cancel remaining legs as well as adjusting the charges.
The British Airways CoC go on to state:
3c5) If you change your transportation without our agreement, your unused flight coupons will not be valid for travel and will have no value and we will not carry you until:
- we or our authorised agents have re-calculated the revised fare for your actual transportation and
- you have paid the difference (if any) between the fare you have already paid and the revised fare which applies to your changed transportation.
If the revised fare is lower than the fare you have already paid, we or our authorised agents will refund you the difference.
3c6) While some changes to your transportation will not result in a change of fare, others, such as changing the place of departure (for example, because you have not used the first flight coupon in your ticket or you have reversed the direction of your travel) may result in a fare increase. Many fares are valid only for travel on the dates and for the flights shown on the ticket. You may not be able to change these at all or only if you pay us an extra fee to do so.
This makes it explicitly clear to me - unless you fly the legs in the order on the ticket, the ticket is invalid until British Airways makes the adjustment to accommodate the changes.