Struggling To Sell Shares Instantly – Any Suggestions? ?

Hello…
I have noticed when selling shares via an online share dealing account (in this case Halifax Share Dealing) that my attempts can be refused on the basis, I assume, of me trying to sell more shares than permitted at the given moment. As I understand it the vloume of shares that can be sold in real-time can vary throughout the day based on demand!
I have had mixed success with this. Sometimes I can sell 4000+ shares without a hitch and other times I am constantly referred to a “Negotiated Trade”.
Are there any Online Share Dealing sites that provide a more reliable service when it comes to selling shares. I would not have considered 4500 shares (£3,000 worth) a lot but there is a good chance I do not have perspective on this matter!
The pessimist in me assumes that the difficulty to sell large numbers of shares in one transaction is a strategy by the Share Dealing Service to increase a greater number of smaller transactions rather than a lesser numbers of larger transactions on the premis that this will generate greater revenue from commission fees! On the flip side I have considered that maybe a transaction for 4500 shares can only be quoted for and go through instantly if there is someone offering to buy!
Can anyone comment? Is this just the way it is or are there sites that provide consistent real-time/instantaneous share purchases and sales regardless of volume?
Thanks in advance for any answers.
Jamie.